# Physics Research Works

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Item INFLUENCE OF THE ELECTROCHEMICAL ENVIRONMENT ON DIFFUSION PROCESSES NEAR STEP AND ISLAND EDGES: Ag(111) and Ag(100)(2000) Haftel, Michael I.; Einstein, Theodore L.The electrochemical cell provides a potentially powerful means of altering morphology and islanding phenomena on metallic surfaces. Diffusion and attachment processes on terraces and near step and island edges are known to profoundly affect island sizes, shapes and coarsening kinetics. Using the surface-embedded-atom-model (SEAM) for describing metallic surfaces in the electrolytic environment, we calculate the dependence of the activation energies for the aforementioned diffusion processes on the deposited surface charge for the Ag(111) and Ag(100) surfaces in an electrolytic environment. While all these processes show some degree of dependence on the potential, the step-edge barrier and the edge diffusion processes are the most sensitive. Step-edge barriers increase (to over 1 eV) with large positive potential (0.85 V), while edge diffusion barriers monotonically decrease with positive surface charge on Ag(100) and Ag(111). We assess the effect these diffusion barriers have on island size/shapes and coarsening dynamics and discuss the implications on electrochemical tuning of islanding phenomena.Item Two-step unconventional protocol for epitaxial growth in one dimension with hindered reactions(American Physical Society, 2019) Sanchez, Julian A.; Gonzalez, Diego Luis; Einstein, Theodore L.We study the effect of hindered aggregation and/or nucleation on the island formation process in a two-step growth protocol. In the proposed model, the attachment of monomers to islands and/or other monomers is hindered by additional energy barriers which decrease the hopping rate of the monomers to the occupied sites of the lattice. For zero and weak barriers, the attachment is limited by diffusion while for strong barriers it is limited by reaction. We describe the time evolution of the system in terms of the monomer and island densities, N1 and N. We also calculate the gap length, the capture zone and the island distributions. For all the sets of barriers considered, the results given by the proposed analytical model are compared with those from kinetic Monte Carlo simulations. We found that the behavior of the system depends on the ratio of the nucleation barrier to the aggregation barrier. The two-step growth protocol allows more control and understanding on the island formation mechanism because it intrinsically separates the nucleation and aggregation processes in different time regimes.Item Kinetic-thermodynamic model for carbon incorporation during step-flow growth of GaN by metalorganic vapor phase epitaxy(American Physical Society, 2019) Inatomi, Y.; Kangawa, Y.; Pimpinelli, Alberto; Einstein, Theodore L.Relationships between concentration of unintentionally doped carbon in GaN and its metalorganic vapor phase epitaxy conditions were investigated theoretically. A kinetic-thermodynamic model which considers kinetic behavior of adsorbed atoms on vicinal surface was proposed.Item Strain-Controlled Magnetic and Optical Properties of Monolayer 2H-TaS e2(American Physical Society, 2019) Chowdhury, Sugata; Simpson, Jeffrey R.; Einstein, Theodore L.; Hight Walker, Angela R.First-principles calculations are used to probe the effects of mechanical strain on the magnetic and optical properties of monolayer (ML) 2H?TaSe2. A complex dependence of these physical properties on strain results in unexpected spin behavior, such as ferromagnetism under uniaxial, in-plane, tensile strain and a lifting of the Raman-active E? phonon degeneracy.Item Patterns of Organics on Substrates with Metallic Surface States: Why? So??(JSVSS, 2018) Einstein, Theodore L.; Bartels, Ludwig; Morales-Cifuentes, Josue R.This paper modestly expands an invited talk at ISSS-8 with the same title. After reviewing the relevant interactions between adsorbates on substrates with metallic surface states (especially Cu(111)), it focuses on organic adsorbates. Of particular interest are those which form honeycomb lattices with pores of various sizes. The nature of the confined states derived from the surface-state electrons is discussed as their effect on admolecules inside the pores.Item Fragmentation approach to the point-island model with hindered aggregation: Accessing the barrier energy(American Physical Society, 2017) Gonzalez, Diego Luis; Pimpinelli, Alberto; Einstein, Theodore L.We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size i. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length la. For la=0 the islands behave as perfect sinks while for la?? they behave as reflecting boundaries. For intermediate values of la, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of i and la. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model (i and la). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of la and i=1, 2, and 3.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 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 Dynamical Scaling Implications of Ferrari, Prähofer, and Spohn’s Remarkable Spatial Scaling Results for Facet-Edge Fluctuations(Springer, 2014) Einstein, Theodore L.; Pimpinelli, AlbertoSpurred by theoretical predictions from Spohn and coworkers (Phys. Rev. E 69, 035102(R) (2004)), we rederived and extended their result heuristically as well as investigated the scaling properties of the associated Langevin equation in curved geometry with an asymmetric potential. With experimental colleagues we used STM line scans to corroborate their prediction that the fluctuations of the step bounding a facet exhibit scaling properties distinct from those of isolated steps or steps on vicinal surfaces. The correlation functions was shown to go as t 0.15(3) decidedly different from the t 0.26(2) behavior for fluctuations of isolated steps. From the exponents, we were able to categorize the universality, confirming the prediction that the non-linear term of the KPZ equation, long known to play a central role in non-equilibrium phenomena, can also arise from the curvature or potential-asymmetry contribution to the step free energy. We also considered, with modest Monte Carlo simulations, a toy model to show that confinement of a step by another nearby step can modify as predicted the scaling exponents of the step’s fluctuations. This paper is an expansion of a celebratory talk at the 95th Rutgers Statistical Mechanics Conference, May 2006.Item Analyzing Capture Zone Distributions (CZD) in Growth: Theory and Applications(Elsevier, 2014) Einstein, Theodore L.; Pimpinelli, Alberto; Gonzalez, Diego LuisItem How "Hot Precursors" Modify Island Nucleation: A Rate-Equation Model(American Physical Society, 2014) Morales-Cifuentes, Josue R.; Einstein, Theodore L.; Pimpinelli, AlbertoWe propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F, assumed to be in a hot precursor state before thermalizing.Item Triangular lattice gas with first- and second-neighbor exclusions: Continuous transition in the four-state Potts universality class(American Physical Society, 1984) Bartelt, N. C.; Einstein, Theodore L.Using phenomenological renormalization (transfer-matrix scaling), we have reexamined the phase transition of a triangular lattice gas with particles having both nearest- and second-nearest-neighbor exclusions. Widely accepted classical studies indicated that disordering of the ordered (p(2x2)) state is first order. In contradiction, we show that the transition is second order; its exponents are consistent with the four-state Potts model universality class, in accord with its Landau-Ginzburg-Wilson Hamiltonian classification.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 Interacting steps with finite-range interactions: Analytical approximation and numerical results(American Physical Society, 2013) Jaramillo, Diego Felipe; Tellez, Gabriel; Gonzalez, Diego Luis; Einstein, Theodore L.We calculate an analytical expression for the terrace-width distribution P(s) for an interacting step system with nearest- and next-nearest-neighbor interactions. Our model is derived by mapping the step system onto a statistically equivalent one-dimensional system of classical particles. The validity of the model is tested with several numerical simulations and experimental results. We explore the effect of the range of interactions q on the functional form of the terrace-width distribution and pair correlation functions. For physically plausible interactions, we find modest changes when next-nearest neighbor interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.Item Mean-field approximation for spacing distribution functions in classical systems(American Physical Society, 2012) Gonzalez, Diego Luis; Pimpinelli, Alberto; Einstein, Theodore L.We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.Item "The Princess and the Pea" at the Nanoscale: Wrinkling and Delamination of Graphene on Nanoparticles(American Physical Society, 2012) Yamamoto, Mahito; Pierre-Louis, O.; Huang, Jia; Fuhrer, Michael S.; Einstein, Theodore L.; Cullen, William G.Thin membranes exhibit complex responses to external forces or geometrical constraints. A familiar example is the wrinkling, exhibited by human skin, plant leaves, and fabrics, that results from the relative ease of bending versus stretching. Here, we study the wrinkling of graphene, the thinnest and stiffest known membrane, deposited on a silica substrate decorated with silica nanoparticles. At small nanoparticle density, monolayer graphene adheres to the substrate, detached only in small regions around the nanoparticles. With increasing nanoparticle density, we observe the formation of wrinkles which connect nanoparticles. Above a critical nanoparticle density, the wrinkles form a percolating network through the sample. As the graphene membrane is made thicker, global delamination from the substrate is observed. The observations can be well understood within a continuum-elastic model and have important implications for strain-engineering the electronic properties of graphene.Item Voronoi cell patterns: Theoretical model and applications(American Physical Society, 2011) Gonzalez, Diego Luis; Einstein, Theodore L.We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car-parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris Métro stations.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 Summary Abstract: Pseudodipole selection rules for extended fine structure in APS: Calculations and applications.(AIP, 1984) Mehl, M. J.; Einstein, Theodore L.; Bryant, G. W.Item Response of the Shockley surface state to an external electrical field: A density-functional theory study of Cu(111)(American Physical Society, 2012) Berland, K.; Einstein, Theodore L.; Hyldgaard, P.The response of the Cu(111) Shockley surface state to an external electrical field is characterized by combining a density-functional theory calculation for a slab geometry with an analysis of the Kohn-Sham wave functions. Our analysis is facilitated by a decoupling of the Kohn-Sham states via a rotation in Hilbert space. We find that the surface state displays isotropic dispersion, quadratic until the Fermi wave vector but with a significant quartic contribution beyond. We calculate the shift in energetic position and effective mass of the surface state for an electrical field perpendicular to the Cu(111) surface; the response is linear over a broad range of field strengths. We find that charge transfer occurs beyond the outermost copper atoms and that accumulation of electrons is responsible for a quarter of the screening of the electrical field. This allows us to provide well converged determinations of the field-induced changes in the surface state for a moderate number of layers in the slab geometry.