Physics

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    MODELING OF INTERFACES: APPLICATIONS IN SURFACE AND POLYMER PHYSICS
    (2013) Patrone, Paul Nathan; Einstein, Theodore L.; Margetis, Dionisios; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In this dissertation, I give an overview of my work on multiscale modeling of interfaces in crystalline and block-copolymer systems. I focus on two distinct interface systems: steps on vicinal surfaces and microdomain interfaces in block- copolymers melts. For each system, I consider how to (i) define the interface, (ii) derive a coarse-grained model of the interface, and (iii) use the model to study morphological features of the interface. For vicinal surfaces, we define a step by means of ensemble averages, which leads to a Burton-Cabrera-Frank (BCF) -type model of surface evolution. Using the BCF model, we study the combined effects of step interactions and fluctuations. For block-copolymers, we define the microdomain interfaces in terms of the relative density of monomers and use the Leibler-Ohta- Kawasaki phase-field Hamiltonian to study the line-edge roughness.
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    Modeling the Anisotropy of Step Fluctuations on Surfaces: Theoretical Step Stiffness Confronts Experiment
    (2006-08-29) Stasevich, Timothy John; Einstein, Theodore L; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In this thesis, we study the anisotropy of step stiffness: an important parameter describing the fluctuations of surface steps within the continuum step model. Using a lattice-gas framework, we derive many practical formulas for the anisotropy of step stiffness on face centered cubic {001} and {111} surfaces. We compare our formulas to experiments on Ag and Cu surfaces and thereby predict the size of nearest-neighbor, next-nearest-neighbor, and three-adatom, non-pairwise "trio" interactions between adatoms. To further corroborate our theory, we perform a series of first-principle calculations of the relevant adatom interactions. We also incorporate our formulas into simulations and model the relaxation of a Ag step initially pinned by surface impurities. Finally, we extend our theory to model Ag steps decorated by C_60 molecules. Together, our work provides a consistent picture of step stiffness anisotropy from an experimental, theoretical, and numerical perspective.
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    Terrace Width Distribution and First Passage Probabilities for Interacting Steps
    (2005-12-05) Bantu, Hailu Gebremariam; Einstein, Theodore L; Chemical Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Stochastic behavior of steps and inter-step distance is studied using Monte Carlo simulation. Terrace-step-kink model is used to represent vicinal surfaces. These vicinal surfaces consist of steps and the space between the steps called terraces. In the first part, the distribution of the width of the terraces and its relation with the strength of step-step interaction is studied. Step positions on vicinal surfaces can be mapped into the world line of fermionic particles in one dimension. The distribution of the inter-particle distance in one dimension is in turn related to the distribution of energy levels one obtains from Random Matrix theory. The energy level distribution in Random Matrix theory is nicely approximated by Wigner distribution for three symmetries described by three parameters. These parameters correspond to the step-step interaction strength in vicinal surfaces. However, when we consider vicinal surfaces the three values of step-step interaction strength are not special. Therefore, they are generalized to include all interaction strengths and it is called the generalized Wigner distribution. The Monte Carlo simulation results show that the generalized Wigner distribution is a very accurate description for the terrace width distribution. Analytical and simulation results of study of the evolution of the variance of the terrace width distribution for different physically interesting and experimentally testable situations are also presented. The analytical result is based on Fokker-Planck formalism obtained from the mapping of the vicinal surfaces into one-dimensional spinless fermionic particles. In the second part, we present the study of the effect of step-step interaction on several scaling laws one obtains from the Langevin formalism of step fluctuations. Based on the limiting processes responsible for fluctuations of isolated step, the mechanisms are divided into three universality classes: attachment-detachment, step-edge diffusion and terrace diffusion. Using Monte Carlo simulation of an attachment-detachment type process, we show that the scaling laws for width of fluctuation, correlation time and survival probabilities are affected by interaction of steps. In contradiction to what one expects from the analytical results obtained using the Gruber-Mullins picture, We also show that the correlation time increases with interaction strength.