Some Problems in the Theory of Crystalline Surfaces
Abstract
This thesis is concerned with the statics and dynamics of free crystalline surfaces. Both unstable and relaxational dynamics are treated with particular attention paid to elastic interactions. An equation of motion for the thermal faceting of an unstable planar crystalline surface is proposed, from which the behavior in the linear region of the surface structure function, initial domain size, and velocity of domain spreading are extracted. Elastic interactions are shown to modify the location of the spinodal line significantly. Solutions for the dynamics of the evaporative decay of onedimensional sine waves, isolated step packets, and isolated facets on surfaces below their roughening transition are presented, which have only the initial time as a free parameter. The solutions are tested against mesoscopic models with excellent agreement found. Intrinsic and reconstructiondriven isolated facet growth are identified as distinct processes, with different equations of motion. The decay of a sine wave is shown to generate a far from equilibrium layer at the top of the sine wave, which has to be separated as a boundary layer. The late stages of thermal faceting of a vicinal surface are shown to lead to a spontaneous breakdown of the coarsegrained free energy. Finite size effects and interface energies resulting from elastic interactions are calculated. Elastic interactions are shown to freeze onedimensional domain ripening in thermal faceting at late times. The elastic displacement field and the corresponding stress and strain tensors of an isolated step are computed and used to measure the surface dipole moments of Si as: d_{x} = 1.46eV/A and d_{z} = 0.58eV/A. The displacement field of a stepped surface is computed. Surface steps on Pb are shown to melt due to the elastic field of a step and as a local wetting transition. The melting of steps, vacancies, and diffusers is shown to account for the anomalous behavior of the Pb equilibrium crystal shape.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT.......241S
 Keywords:

 ELASTIC INTERACTIONS;
 THERMAL FACETING;
 Physics: General; Physics: Condensed Matter