The Structure and Dynamics of Surfaces and Overlayers with One-Dimensional Misfit.

I present the results of a comprehensive numerical investigation of one-dimensional misfit dislocations as modelled by discrete versions of the classical sine-Gordon and double-sine-Gordon non-linear wave equations. Such systems find applications in the study of clean-reconstructed and adsorbate-covered surfaces. These models can also be applied to many other low-dimensional systems characterized by competing periodicities, such as intercalated graphite and charge density waves. Employing molecular dynamics and numerical fast Fourier transform techniques, I investigate both the structure and dynamics of such systems. The structural studies include the energetics of both stable and metastable equilibrium chain configurations, the commensurate-incommensurate phase transition, and the effects of discreteness. The dynamical investigations focus on the dispersion of the vibrational modes of phonons, misfit dislocations and their coupling, as well as on pinning, the effects of discreteness, internal kink degrees of freedom, and non-linear oscillation.