Tracer diffusion of oxygen in YBa2Cu3O7-x from Monte Carlo simulations of an Ising-type model.
Gumede, Stephen Napolian Zibusiso.
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In the research reported here, a two-dimensional Ising-type model was used to study the tracer diffusion coefficients of oxygen ions in YBa2Cu307-x (YBCO) for various values of oxygen concentration and temperature. The first chapter provides a brief introduction to the problem considered in this thesis. This is followed by a short review of superconductivity, with particular reference to the experimental and theoretical aspects of high-temperature superconductivity and its applications. The structure of YBCO is then presented, with emphasis on its behaviour for various values of oxygen concentration and temperature. The model used in the simulations and the results for tracer diffusion coefficients and related quantities obtained by previous workers concludes the chapter. Results from other theoretical models are also included. In the second chapter a theoretical background for the Monte Carlo simulations employed in the present investigation is discussed. This chapter includes a short account on how these numerical methods evolved. The Monte Carlo approach to numerical evaluation of integrals is described. Then the idea of Markov sampling for obtaining members of the canonical ensemble is presented, and the Metropolis algorithm is described. In particular, convergence and the detailed balance condition are discussed. The consequence of starting from an arbitrary initial state when evaluating an observable of interest, and the effect on the reliability of the values of observables, are analysed. The chapter closes with a discussion of Monte Carlo methods applied to a lattice model in statistical mechanics. In chapter three results for the oxygen distribution produced by the diffusion of oxygen in YBCO are presented. These results were obtained from Monte Carlo simulations of the anti-symmetric nextto- nearest neighbour Ising (ASYNNNI) model. In addition to the uniform equilibrium distributions obtained by previous workers, it is found that this model also possesses nonuniform equilibrium oxygen distributions. The nonuniform distributions show a rich phase structure, and some preliminary results for this structure are presented. Results for the tracer diffusion coefficients in the nonuniform equilibrium distributions are given in the last chapter. Both local and global tracer diffusion coefficients for nonuniform equilibrium configurations are presented. Results obtained for uniform and nonuniform equilibrium configurations are compared.