Doctor of Philosophy (PhD)


Engineering Science (Interdepartmental Program)

Document Type



This dissertation can be divided into four parts. In part I (Chapter 2), the diffusion controlled growth of multiple compound phases is studied with the nonlinear Kirkendall effect included. This part analyzes the growth of N compound phases. The method of finding intrinsic diffusion coefficients from only the positions of interfaces is found for two layers. In addition, the asymptotic analysis valid for small concentration gradients is applied to the “multi-foil” method of measuring intrinsic diffusion coefficients and yields an analytic solution for the displacement curve. A bounded solid film on a substrate can breakup from the edge into islands to reduce the surface energy. Part II (Chapter 3) studies the three-dimensional linear stability of a retracting film profile. An unstable mode of perturbation is found. The perturbed film profile is wavy along the film edge which can initiate the formation of “fingers” seen in experiments. The wavelength of the fastest growing perturbation agrees with the distance between two adjacent islands observed in experiments. Part III (Chapter 4) studies the linear stability of square or triangular wires with azimuthal surface energy anisotropy. The growth rate of a normal mode is governed by an eigenvalue problem, which is solved numerically by a pseudospectral method. The fundamental and first modes, which correspond to varicose(sausage) and helical modes, are unstable for long wavelengths. The varicose mode has the highest growth rate for the range of parameters investigated. The maximum growth rate increases with anisotropy, implying that the anisotropy is destabilizing. An asymptotic solution is derived in the limit of zero anisotropy, and it agrees with the numerical solutions. The results obtained here for wires also apply to channels. Part IV (Chapter 5) investigates Rayleigh’s instability of nano wires by classic molecular dynamic simulations. The melting point of nanowires with different radii is found by calculating the caloric curve and mean square displacement curve. Liquid and solid nano-wires with different radii are simulated. It shows that liquid wires breakup following Rayleigh’s instability criterion, whereas solid wires don’t.



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Committee Chair

Harris Wong