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. / Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1998.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/5779 |
| Date | January 1998 |
| Creators | Gumede, Stephen Napolian Zibusiso. |
| Contributors | Ilchev, A. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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