Physics
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Item Unified view of step-edge kinetics and fluctuations(American Physical Society, 1998) Khare, S. V.; Einstein, Theodore L.We study theoretically the equilibrium fluctuations of steps on vicinal surfaces. From an analytical continuum description of the step edge, we find a single Langevin equation governing the motion of an isolated step around its equilibrium position that includes attachment/detachment of atoms, diffusion over the terrace, diffusion along the edge, and evaporation. We then extend this approach to treat an array of steps, i.e., a vicinal surface. We also present, in an appendix, an alternative formalism in which detachment to terrace and to step-edge diffusion can take place independently. In established as well as some new limits, and for numerous special cases, we study the wave-vector dependence—both exponent and prefactor—of the relaxation time of fluctuations. From this we recover scaling relations for early-time dependence of the mean-square fluctuations. We discuss how to extract the (mesoscopic) transport coefficients associated with different atomistic mechanisms of surface mass transport and how to distinguish between mechanisms having the same power-law dependence on wavelength in the capillary-wave analysis. To examine the crossovers between limiting regimes, we compute and explore an effective exponent for this power law and show that the crossover occurs over a narrow region of phase space. Furthermore, we find that single-sided approximations are valid only in the limit of extreme Schwoebel barriers.Item Stress Relief in Reconstruction(American Physical Society, 1997) Bach, Claudia E.; Giesen, Margret; Ibach, Harald; Einstein, Theodore L.We report on the first direct measurement of the change of the surface stress in the reconstruction of the Au(111) and the Au(100) surfaces. For both surfaces the reconstruction relaxes the intrinsic tensile stress, by 22 percent and 5 percent, respectively. A discussion of the data on the Au(111) surface in the Frenkel-Kontorova model shows that the energy gain due to the surface stress is not quite large enough to make the reconstructed phase energetically favored without the formation of the secondary herringbone structure of the solitons. On the Au(100) surface, the gain in elastic strain energy is clearly insufficient to cause the surface to reconstruct.Item Edge Diffusion during Growth: The Kink Ehrlich-Schwoebel Effect and Resulting Instabilities(American Physical Society, 1999) Pierre-Louis, O.; D'Orsogna, M. R.; Einstein, Theodore L.The morphology of surfaces of arbitrary orientation in the presence of step and kink Ehrlich-Schwoebel effects (SESE and KESE) during growth is studied within the framework of a model in which steps are continuous lines, and is illustrated by a simple solid-on-solid model. For vicinal surfaces KESE induces an instability often stronger than that from SESE. The possibility of stable kink flow growth is analyzed. Fluctuations can shift the stability threshold. KESE also induces mound formation.Item Bending-rigidity-driven transition and crumpling-point scaling of lattice vesicles(American Physical Society, 1996) Orlandini, E.; Stella, A. L.; Einstein, Theodore L.; Tesi, M. C.; Beichl, I.; Sullivan, F.Item Oscillatory interaction of steps on W(110)(American Physical Society, 1996) Xu, Wei; Adams, James B.; Einstein, Theodore L.Using a modified fourth-moment approximation to tight-binding theory, we have carried out a systematic study of the energetics of steps and kinks on the W(110) surface. This model predicts an oscillatory interaction (as a function of separation) between isolated stable steps on the W(110) surface, whereas previous studies of step-step interactions on late transition and noble metals with the embedded atom method found a purely repulsive, inverse-square decay. The oscillations are similar to those found by scanning tunneling microscope measurements of vicinal Cu(100) and Ag(110) systems.Item Phase diagram of a two-dimensional lattice-gas model of oxygen ordering in YBa2Cu3Oz, with realistic interactions(American Physical Society, 1995) Liu, D. J.; Einstein, Theodore L.; Sterne, P. A.; Wille, L. T.We have determined a first-principles temperature-composition phase diagram describing the ordering of oxygen atoms in the "chain" layers of YBa2Cu3Oz. The calculations are based on a transfer-matrix finite-size-scaling study of a two-dimensional lattice-gas Hamiltonian (the asymmetric next-nearest-neighbor Ising (ASYNNNI) model). The interaction parameters are obtained from ab initio electronic structure calculations. The resulting phase diagram compares favorably with experiment. We analyze its sensitivity to the relative size of the interactions. We also show that the addition of a third-neighbor interaction has a minimal effect on the phase boundaries. Based on these results, we assess the applicability of the ASYNNNI model to YBa2Cu3Oz.Item Diffusion of Monolayer Adatom and Vacancy Clusters: Langevin Analysis and Monte Carlo Simulations of their Brownian Motion(American Physical Society, 1995) Khare, S. V.; Einstein, Theodore L.; Bartelt, N. C.In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius R, the cluster diffusion constant varies as R1 and R2. From an analytical Langevin description of the cluster's steplike boundary, we find three cases, R1, R2, and R3, corresponding to the three microscopic surface mass-transport mechanisms of straight steps. We thereby provide a unified treatment of the dynamics of steps and of clusters. For corroboration, we perform Monte Carlo simulations of simple lattice gases and derive atomistic diffusion constants.Item Brownian motion and shape fluctuations of single-layer adatom and vacancy clusters on surfaces: Theory and simulations(American Physical Society, 1996) Khare, S. V.; Einstein, Theodore L.In recent observations of Brownian motion of islands of adsorbed atoms and of vacancies with mean radius R, the cluster diffusion constant Dc varies as R1 and R2. From an analytical continuum description of the cluster's steplike boundary, we find a single Langevin equation for the motion of the cluster boundary, rather than three special cases.Item Dynamics of step doubling: simulations for a simple model and comparison with experiment(Elsevier, 1995) Khare, S. V.; Einstein, Theodore L.; Bartelt, N. C.To interpret recent experiments on the dynamics of step doubling, we have studied a simple model of this phase transition. With Monte Carlo, we compute the time-dependence of the order parameter in the limit of rapid diffusion across terraces. Analysis of the data shows that the limiting step is the time for adjacent steps to touch each other; subsequent "zipping" together happens rapidly. From this vantage we develop an analytic expression for short times that changes into a phenomenological one for later times. Using data from two physical systems, we compare this function and another based on naive assumptions with a third based on chemical rate theory. For the more recent data, our expression describes the data best. Finally, in the opposite limit in which atoms can only move along step edges, we show characteristic configurations and compute the structure factor.Item Self-avoiding surfaces, topology, and lattice animals(American Physical Society, 1992) Stella, A. L.; Orlandini, E.; Beichl, I.; Sullivan, F.; Tesi, M. C.; Einstein, Theodore L.With Monte Carlo simulation we study closed self-avoiding surfaces (SAS) of arbitrary genus on a cubic lattice.