arXiv subjects

Wolfgang Kappus

Publications and source records attributed to Wolfgang Kappus.

11 recordsLinked to original sources

arXiv2020

Harmonic mesh modelling of hexagonal FeN stripes on Cu(001)

Hexagonal FeN monolayers on Cu(001) show a stripe pattern composed of dark and bright stripes as observed recently by scanning tunneling microscopy (STM). Here a harmonic mesh model is proposed to interpret those results. It uses a planar Fourier analysis with two different wave vectors to calculate small displacements of Fe atoms caused by lattice mismatch stress. The area of displaced Fe atom triangles is used as a measure for the protrusion of N atoms in their center. Proper selection of the wave vectors allows to visualize the dominant protrusions of (Sqrt(3) x Sqrt(3)) ordered nitrogen atoms. The wave vectors selected are related to Fe configurations which minimize lattice mismatch stress. The model is kept simple, so just the most basic features of the STM experiments are covered. The limits of the model are discussed and ways for extending it are proposed.

cond-mat.mtrl-sci↗

arXiv2020

Adatom generated spatially oscillating strain fields on isotropic and other substrates

An extended elastic eigenvector approach for adatom interactions is applied to elastically isotropic substrates. The oscillating interactions between adatom monomers or dimers are caused by strain fields in the substrate. Expansive or contractive strain fields are surrounding adatoms in form of quasi circular rings. The exact shape of the ring structure depends on the elastic constants of the substrate and especially on the surface Brillouin zone. Interactions on isotropic substrates are depicted and compared with an anisotropic example. Overlays of 2-D plots can help to identify adatom structures caused by elastic effects and to prepare numerical calculations of their elastic energies. The consequences of different sorts of adatoms with different interaction sign are sketched, large short distance attraction could occur in such cases. Limitations of the method are discussed and possible applications are formulated.

cond-mat.mtrl-sci↗

arXiv2020

Modelling the size of Nitrogen c(2x2) islands on Cu(001) with elastic multisite interactions

An extended elastic eigenvector approach for adatom interactions is applied to model Nitrogen c(2x2) Atom islands on Cu(001). Oscillating interactions between adatom monomers or dimers are considered. Attractive pair interactions of adatoms are able to describe agglomeration but fail to explain the size of islands. Multisite interactions created by dimers, however, can explain the size of islands if an interaction parameter is adjusted properly. Finite size islands are formed when repulsive monomer interactions are balanced by attractive monomer-dimer interactions. A simple model of nearest neighbour attraction and s-3 repulsion is used as an example for the interaction parameter search. Previous experimental studies have shown that in the low coverage region Nitrogen atoms agglomerate to isolated square islands of about 5 nm x 5 nm size with a c(2x2) structure. With increasing coverage those islands form regular patterns but do not touch below about 0.4 monolayers. Previous experiments and calculations have shown that the square island pattern show significant elastic effects. Different adatom structures within the Nitrogen islands have been analyzed, a dimer step model is able to reproduce the experimentally found island size. This model requires a molecular bond between dimers formed by Nitrogen adatoms. The model is also used to compute elastic interactions between islands and to check it against the experimentally found island pattern. Shortcomings and limitations of the model are discussed and open questions are formulated.

cond-mat.mtrl-sci↗

arXiv2019

Elastic interactions of Fe adatoms on Cu(111) at the mesoscale

An extended elastic eigenvector approach had earlier been developed to interpret ab-initio calculations of adatom interactions. It shows oscillating interactions as well as trio- and quarto (multisite) terms within clusters. It is now applied to the interaction of Fe adatoms on Cu(111). The extended approach differs from previous calculations by using a sharp cutoff - generating oscillating interactions - and by taking into account interacting dimers - generating strong anisotropies and multisite terms. Additional weak anisotropy stems from the substrate and from the surface Brillouin zone shape. This approach has 3 free parameters which have been fitted to first principles interactions of Fe adatoms on Cu(111). Elastic adatom pair interactions and dimer-dimer interactions at mesoscale separations show a reasonable good fit to the first principles interactions. At smaller separations elastic interaction values remain questionable. To enable a comparison with future first principle calculations also dimer-monomer interactions are shown. Some conclusions on initial adatom formation and diffusion are proposed and open questions are formulated.

cond-mat.mtrl-sci↗

arXiv2019

Adatom pair distribution up to half coverage: O-Pd(100)

The superposition approximation and the Born-Green-Yvon (BGY) equation allows calculation of pair distributions in thermal equilibrium from pair potentials. A 2-d variant can be used to derive adatom pair distributions from arbitrary analytical pair potentials. As practical example substrate mediated elastic interactions, fitted previously to first principles (FP) calculations, are used to derive adatom pair distributions of OPd(100). The evaluation method utilizes the particle-hole symmetry of the pair interaction lattice gas Hamiltonian. The nonlinear BGY-type integral equation is solved numerically up to half coverage using power series expansion of coverage. The resulting adatom pair- and three-body distributions are used to analyze the short-range order of adatoms. A Monte Carlo (MC) simulation was performed in parallel to compare the current model with established methods. MC derived pair distributions fit well to those found with the analytical model, except in the high coverage region. The Fourier transformed pair correlations are compared with experimental LEED spot data and provide additional insight. Due to significant attraction the model predicts formation of 3rd and 4th nearest neighbors (n.n.) at small 3rd n.n. chains. A long range order of adatoms like a p(2x2) lattice is not found with the current model but a glassy structure is proposed as also indicated by the equilibrium Monte Carlo configurations. The glassy structure is assumed to contain fluctuations explaining broad p(2x2) LEED spots in the 0.25 monolayer region. The assumptions and limitations of the model towards higher coverages are discussed and open questions are formulated.

cond-mat.mtrl-sci↗

arXiv2017

First-principles lattice-gas Hamiltonian revisited: O-Pd(100)

The methodology of deriving an adatom lattice-gas Hamiltonian (LGH) from first principles (FP) calculations is revisited. Such LGH cluster expansions compute a large set of lateral pair-, trio-, quarto interactions by solving a set of linear equations modelling regular adatom configurations and their FP energies. The basic assumption of truncating interaction terms beyond fifth nearest neighbors does not hold when adatoms show longer range interactions, e.g. substrate mediated elastic interactions. O-Pd(100) as a popular reference is used to propose a long range elastic interaction alternative including many-body trio- and quarto terms with just 3 parameters fitted to FP calculations. A key feature of the interaction alternative is its analytic nature, allowing statistical methods different from Monte Carlo simulations to derive surface order. The assumptions made are discussed and ways to further verify and apply the model are outlined.

cond-mat.mtrl-sci↗

arXiv2016

Strain mediated interaction of adatom dimers

An earlier model for substrate strain mediated interactions between monomer adatoms is extended to the interaction of monomers with dimers and the interaction of dimers. While monomers (sitting on high symmetric sites) are supposed to create isotropic stress on the substrate, dimers would create anisotropic stress caused by stretching their bond. Resulting interactions are strongly angle dependent and also reflect the elastic anisotropy of the substrate. The applicability of a continuum elastic model and its limitations are discussed. Consequences for modelling adatom structures are sketched without detailed analysis.

cond-mat.mtrl-sci↗

arXiv2016

Strain mediated tri- and quattro- interactions of adatoms

Lateral interactions of oxygen adatoms derived from first-principles calculations of the O-Pd(100) system had been claimed to include trio- and quattro terms beside pair interactions. This paper is dedicated to extend an earlier model for substrate strain mediated interactions between adatom pairs to include trio- and quattro terms. While monomers (sitting on high symmetric sites) are supposed to create isotropic stress on the substrate, dimers would create anisotropic stress. The requirement of mechanical equilibrium allows to formulate the elastic energy as a sum of pair-, trio- and quattro terms, solved by respective an eigenvalue problems. Resulting interactions are strongly angle dependent and also reflect the elastic anisotropy of the substrate. A continuum elastic model supports the long range character of the elastic interaction but should also describe some short range features. For the elastically isotropic tungsten substrate a closed solution for quattro interactions is presented, for trio inter cations numerical values are given.

cond-mat.mtrl-sci↗

arXiv2013

Strain mediated adatom stripe morphologies on Cu<111> simulated

Substrate strain mediated adatom configurations on Cu<111> surfaces have been simulated in a coverage range up to nearly 1 monolayer. Interacting adatoms occupy positions on a triangular lattice in two dimensions. The elastic interaction is taken from earlier calculations, short range effects are added for comparison. Dependent on the coverage different morphologies are observed: Superlattices of single adatoms in the 0.04 ML region, ordered adatom clusters in the 0.1 ML region, elongated islands in the 0.3 ML region, and interwoven stripes in the 0.5 ML region. In the region above the sequence is reversed with occupied and empty positions complemented. Stronger short range interactions increase the feature size of the clusters and reduce their lattice order. The influence of the substrate elastic anisotropy turns out to be significant. Results are compared with morphologies observed on Cu<111> surfaces and the applicability of the model is discussed.

cond-mat.mtrl-sci↗

arXiv2012

Stability and Dynamic of strain mediated Adatom Superlattices on Cu<111>

Substrate strain mediated adatom density distributions have been calculated for Cu<111> surfaces. Complemented by Monte Carlo calculations a hexagonal close packaged adatom superlattice in a coverage range up to 0.045 ML is derived. Conditions for the stability of the superlattice against nucleation and degradation are analyzed using simple neighborhood models. Such models are also used to investigate the dynamic of adatoms within their superlattice neighborhood. Collective modes of adatom diffusion are proposed from the analogy with bulk lattice dynamics and methods for measurement are suggested. The explanation of surface state mediated interactions for superstructures found in scanning tunnelling microscopy experiments is put in question.

cond-mat.mtrl-sci↗

arXiv2012

Strain Induced Adatom Correlations

A Born-Green-Yvon type model for adatom density correlations is combined with a model for adatom interactions mediated by the strain in elastic anisotropic substrates. The resulting nonlinear integral equation is solved numerically for coverages from zero to a limit given by stability constraints. W, Nb, Ta and Au surfaces are taken as examples to show the effects of different elastic anisotropy regions. Results of the calculation are shown by appropriate plots and discussed. A mapping to superstructures is tried. Corresponding adatom configurations from Monte Carlo simulations are shown.

cond-mat.mtrl-sci↗