Browsing by Author "Einstein, Theodore L."
Now showing 1 - 20 of 98
Results Per Page
Sort Options
Item A facet is not an island: step-step interactions and the fluctuations of the boundary of a crystal facet(Elsevier, 2005) Pimpinelli, Alberto; Degawa, M.; Einstein, Theodore L.; Williams, Ellen D.Item Adsorbates in a Box: Titration of Substrate Electronic States(American Physical Society, 2010) Cheng, Zhihai; Wyrick, Jonathan; Luo, Miaomiao; Sun, Dezheng; Kim, Daeho; Zhu, Yeming; Lu, Wenhao; Kim, Kwangmoo; Einstein, Theodore L.; Bartels, LudwigNanoscale confinement of adsorbed CO molecules in an anthraquinone network on Cu(111) with a pore size of ?4??nm arranges the CO molecules in a shell structure that coincides with the distribution of substrate confined electronic states. Molecules occupy the states approximately in the sequence of rising electron energy. Despite the sixfold symmetry of the pore boundary itself, the adsorbate distribution adopts the threefold symmetry of the network-substrate system, highlighting the importance of the substrate even for such quasi-free-electron systems.Item Analysis of terrace-width distributions using the generalized Wigner surmise: Calibration using Monte Carlo and transfer-matrix calculations(American Physical Society, 2004) Gebremariam, Hailu; Cohen, Saul D.; Richards, Howard L.; Einstein, Theodore L.Measurement of terrace-width distributions (TWD’s) of vicinal surfaces is used routinely to find the dimensionless strength à of the elastic repulsion between steps. For sufficiently strong repulsions, the TWD can be described by a Gaussian about the mean step spacing, but controversy has arisen on the correct prefactor in the relation of the TWD variance to Ã. Instead of the various Gaussian approximations, we have advocated for several years that the TWD be fit with the generalized Wigner distribution, essentially a gamma distribution in the normalized squared TWs. The basis for this idea stems from a mapping of the step model to the Sutherland model of fermions in one dimension. While several applications to experiment have been successful, definitive comparison of the various approximations requires high-quality numerical data. We report transfer matrix and extensive Monte Carlo simulations of terrace-step-kink models to support our contentions. Our work includes investigation of finite-size effects and of the breakdown of the continuum picture for values of à larger than in typical experiments.Item Analytic Formulas for the Orientation Dependence of Step Stiffness and Line Tension: Key Ingredients for Numerical Modeling(SIAM, 2006) Stasevich, T. J.; Einstein, Theodore L.We present explicit analytic, twice-differentiable expressions for the temperature-dependent anisotropic step line tension and step stiffness for the two principal surfaces of face-centered-cubic crystals, the square (001) and the hexagonal (111). These expressions improve on simple expressions that are valid only for low temperatures and away from singular orientations. They are well suited for implementation into numerical methods such as finite-element simulation of step evolution.Item Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications(Elsevier, 2014) Einstein, Theodore L.; Pimpinelli, Alberto; Gonzalez, Diego LuisItem Angular momentum branching ratios for electron-induced ionization: Atomic and model calculations(American Physical Society, 1987) Mehl, M. J.; Einstein, Theodore L.We present calculations of the matrix elements for electron-induced ionization of core electrons of atoms. We use both self-consistent atomic potentials for accuracy and model potentials to gain physical insight. We pay particular attention to the angular momentum distribution of the two final-state electrons, especially when one of them lies near what would be the Fermi energy in a solid (i.e., as in an absorption fine-structure experiment). For nodeless core wave functions, in the dominant channel both final-state electrons have angular momentum one greater than that of the initial core state. For sufficiently deeply bound states, this first approximate selection rule holds until the incident electron energy exceeds the ionization threshold by at least 500 eV, i.e., over the experimentally relevant range. It is also possible to determine the angular momentum distribution of the final-state electron. The EXAFS-like electron tends to have angular momentum one greater than that of the initial core state, even in some cases where the first approximate selection rule does not hold. (EXAFS is extended x-ray-absorption fine structure.) The strongest trend is that the dipole component in a partial-wave expansion of the Coulomb interaction dominates the matrix element. In these studies, careful treatment of not just the core state but also the unbound states is crucial; we show that the conventional orthogonalized plane-wave approximation is inadequate, giving incorrect ordering of the channels. For model potentials with an adjustable screening length, low-lying bound resonances are found to play an important role.Item Anisotropic surface-state-mediated RKKY interaction between adatoms(American Physical Society, 2012) Patrone, Paul N.; Einstein, Theodore L.Motivated by recent numerical studies of Ag on Pt(111), we derive an expression for the RKKY interaction mediated by surface states, considering the effect of anisotropy in the Fermi edge. Our analysis is based on a stationary phase approximation. The main contribution to the interaction comes from electrons whose Fermi velocity vF is parallel to the vector R connecting the interacting adatoms; we show that, in general, the corresponding Fermi wave vector kF is not parallel to R. The interaction is oscillatory; the amplitude and wavelength of oscillations have angular dependence arising from the anisotropy of the surface-state band structure. The wavelength, in particular, is determined by the projection of this kF (corresponding to vF) onto the direction of R. Our analysis is easily generalized to other systems. For Ag on Pt(111), our results indicate that the RKKY interaction between pairs of adatoms should be nearly isotropic and so cannot account for the anisotropy found in the studies motivating our work. However, for metals with surface-state dispersions similar to Be(10¯10), we show that the RKKY interaction should have considerable anisotropy.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 Beyond the Wigner distribution: Schrodinger equations and terrace width distributions(American Physical Society, 2005) Richards, Howard L.; Einstein, Theodore L.The so-called generalized Wigner distribution has earlier been shown to be an excellent approximation for the terrace width distribution (TWD) of vicinal surfaces characterized by step-step interactions that are perpendicular to the average step direction and fall off as the inverse square of the step spacing. In this paper, we show that the generalized Wigner distribution can be derived from a plausible, phenomenological model in which two steps interact with each other directly and with other steps through a position-dependent pressure. We also discuss generalizations to more general step-step interactions and show that the predictions are in good agreement with TWDs derived from numerical transfer-matrix calculations and Monte Carlo simulations. This phenomenological approach allows the step-step interaction to be extracted from experimental TWDs.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 Brownian motion of steps on Si(111)(American Physical Society, 1993) Bartelt, N. C.; Goldberg, J. L.; Einstein, Theodore L.; Williams, Ellen D.; Heyraud, J. C.; Metois, J. J.Step motion on surfaces can now be measured quantitatively. We present a formalism for analyzing equilibrium step fluctuations and apply it to real-time reflection electron microscope observations of step motion on Si(111). The time correlation functions of the step positions and of their Fourier components are compared with predictions from Langevin equations for two extreme mechanisms for step motion: edge diffusion and terrace exchange.Item Capture-Zone Scaling in Island Nucleation: Universal Fluctuation Behavior(American Physical Society, 2007) Pimpinelli, Alberto; Einstein, Theodore L.In island nucleation and growth, the distribution of capture zones (in essence proximity cells) can be described by a simple expression generalizing the Wigner surmise (power-law rise, Gaussian decay) from random matrix theory that accounts for spacing distributions in a host of fluctuation phenomena. Its single adjustable parameter, the power-law exponent, can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory elucidates the result.Item Changes in density of states caused by chemisorption(American Physical Society, 1975) Einstein, Theodore L.The process of chemisorption is studied via the change in density of states when an adatom with a single level Ea bonds by a hopping parameter V to the (100) surface of an s-band simple cubic crystal. As V increases, the bond changes from a perturbative regime to the formation of a surface complex. Investigations of local and layer-summed show this dimerlike structure to be well localized near the bond. Steric effects (binding-site symmetry) are easily introduced. A damping parameter can be added to simulate decay effects of surface probes. Application of the model to photoemission angular-averaged and angular-resolved difference spectra for light gases on tungsten gives understanding of the bonding peak near the bottom of the band, of the depletion of states near the Fermi energy, and of the slight shifting of the energy-momentum-conserving peak.Item Chemical insight from density functional modeling of molecular adsorption: Tracking the bonding and diffusion of anthracene derivatives on Cu(111) with molecular orbitals(AIP, 2015) Wyrick, Jonathan; Einstein, Theodore L.; Bartels, LudwigWe present a method of analyzing the results of density functional modeling of molecular adsorption in terms of an analogue of molecular orbitals. This approach permits intuitive chemical insight into the adsorption process. Applied to a set of anthracene derivates (anthracene, 9,10-anthraquinone, 9,10-dithioanthracene, and 9,10-diselenonanthracene), we follow the electronic states of the molecules that are involved in the bonding process and correlate them to both the molecular adsorption geometry and the species’ diffusive behavior. We additionally provide computational code to easily repeat this analysis on any system.Item Coalescence of 3-phenyl-propynenitrile on Cu(111) into interlocking pinwheel chains(AIP, 2011) Luo, Miaomiao; Lu, Wenhao; Kim, Daeho; Chu, Eric; Wyrick, Jon; Holzke, Connor; Salib, Daniel; Cohen, Kamelia D.; Cheng, Zhihai; Sun, Dezheng; Zhu, Yeming; Einstein, Theodore L.; Bartels, Ludwig3-phenyl-propynenitrile (PPN) adsorbs on Cu(111) in a hexagonal network of molecular trimers formed through intermolecular interaction of the cyano group of one molecule with the aromatic ring of its neighbor. Heptamers of trimers coalesce into interlocking pinwheel-shaped structures that, by percolating across islands of the original trimer coverage, create the appearance of gear chains. Density functional theory aids in identifying substrate stress associated with the chemisorption of PPN's acetylene group as the cause of this transition.Item Comment on "Reliability of low-energy electron diffraction for studies of surface order-disorder phenomena"(American Physical Society, 1986) Bartelt, N. C.; Einstein, Theodore L.; Roelofs, L. D.A Comment on the Letter by W. Moritz and M. G. Lagally, Phys. Rev. Lett. 56, 865 (1986).Item Competing growth processes induced by next-nearest-neighbor interactions: Effects on meandering wavelength and stiffness(American Physical Society, 2017) Blel, Sonia; Hamouda, Ajmi BH.; Mahjoub, B.; Einstein, Theodore L.In this paper we explore the meandering instability of vicinal steps with a kinetic Monte Carlo simulations (kMC) model including the attractive next-nearest-neighbor (NNN) interactions. kMC simulations show that increase of the NNN interaction strength leads to considerable reduction of the meandering wavelength and to weaker dependence of the wavelength on the deposition rate F. The dependences of the meandering wavelength on the temperature and the deposition rate obtained with simulations are in good quantitative agreement with the experimental result on the meandering instability of Cu(0 2 24) (T. Maroutian et al., Phys. Rev. B 64, 165401 (2001)). The effective step stiffness is found to depend not only on the strength of NNN interactions and the Ehrlich-Schwoebel barrier, but also on F. We argue that attractive NNN interactions intensify the incorporation of adatoms at step edges and enhance step roughening. Competition between NNN and nearest-neighbor interactions results in an alternative form of meandering instability which we call “roughening-limited” growth, rather than attachment-detachment-limited growth that governs the Bales-Zangwill instability.Item Correlations in nanoscale step fluctuations: Comparison of simulation and experiments(American Physical Society, 2006) Szalma, F.; Dougherty, D. B.; Degawa, M.; Williams, Ellen D.; Haftel, Michael I. Haftel; Einstein, Theodore L.We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo (MC) algorithm, with a two-parameter expression for energy barriers, and compare with our variable-temperature scanning tunneling microscopy line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC simulations and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.Item Critical Exponents of a Four-State Potts Chemisorbed Overlayer: p(2x2) Oxygen on Ni(111)(American Physical Society, 1981) Roelofs, L. D.; Kortan, A. R.; Einstein, Theodore L.; Park, Robert L.We report the first determination of critical exponents for a chemisorbed overlayer, using low-energy electron diffraction. We examine the order-disorder transition of p(2x2) oxygen on the (111) surface of nickel. This study is the first of critical behavior of a two-dimensional system in the four-state Potts universality class. Discussion of disparity between our results and predicted exponents considers several possibilities, including logarithmic corrections.Item Decay of Silicon Mounds: Scaling Laws and Description with Continuum Step Parameters(American Physical Society, 2000) Ichimiya, A.; Hayashi, K.; Williams, Ellen D.; Einstein, Theodore L.; Uwaha, M.; Watanabe, K.The decay of mounds about a dozen layers high on the Si(111)?(7x7) surface has been measured quantitatively by scanning tunneling microscopy and compared with analytic predictions for the power-law dependence on time predicted for a step-mediated decay mechanism. Conformably, we find an exponent 1/4 associated with the (3D) decay of the mound height and exponent 1/3 associated with the (2D) decay of top-layer islands. Using parameters from a continuum step model, we capture the essence of the kinetics. Qualitative features distinguish these mounds from multilayer islands found on metals.