C. Uebing

Determination of surface diffusion coefficients by Monte Carlo methods: Comparison of fluctuation and Kubo–Green methods

A comparison of the Kubo–Green and fluctuation methods for determining surface diffusion coefficients of adsorbates was carried out by Monte Carlo simulations on a square lattice for various adsorbate–adsorbate nearest‐and‐next‐nearest neighbor interactions. Even in ordered regions of the phase diagrams both methods agree, when the system has been fully equilibrated and nearly so if it has not, provided that the ‘‘local’’ mean square fluctuation is used in the Kubo–Green method for the latter situation. Both the mean square fluctuations and D were found to be extremely sensitive to even small deviations from equilibrium near θ=0.5 below Tc. It was also found that the tracer and jump diffusion coefficients are nearly identical under all conditions. The present work was made possible by the enormous computing power of the Julich Intel Paragon computer, which allowed both diffusion and equilibration simulations to be carried out simultaneously in the canonical ensemble. Thus the discrepancy between the two m...

Surface segregation on Fe3%Si0.04%VC(100) single crystal surfaces

Abstract Surface segregation phenomena on (100) oriented single crystal surfaces of the ferritic Fe-3%Si-0.04%V-C alloy were investigated by AES and LEED. At temperatures below 635 °C vanadium and carbon cosegregation is observed after prolonged heating. At thermodynamic equilibrium the substrate surface is saturated with the binary surface compound VC. The two-dimensional VC is epitaxially arranged on the substrate surface as indicated by LEED investigations. Its structure corresponds to the (100) plane of the three-dimensional VC with rocksalt structure. Sharp above 635 °C the surface compound VC is dissolved into the bulk. At higher temperatures the substrate surface is covered with segregated silicon forming a c(2 × 2) structure. This surface phase transition is reversible. Because of the low concentration and slow diffusion of vanadium, non-equilibrium surface states are formed as intermediates upon segregation of silicon and carbon. Below 500 °C a disordered graphite layer with a characteristical asymmetrical C Auger peak is observed on the substrate surface. Above 500 °C carbon segregation leads to the formation of an ordered c(2 × 2) structure with a symmetrical C Auger peak being characteristic for carbidic or atomically adsorbed species. At increasing temperatures silicon segregation takes place leading to a c(2 × 2) structure. Between silicon and carbon site competition is effective.

The diffusion of oxygen on W(110) The influence of the p(2 × 1) ordering

Tracer and chemical surface diffusion coefficients for oxygen chemisorbed on W(110) have been investigated by means of Monte Carlo modeling, taking full advantage of the numerical power of a supermassive parallel supercomputer. The simulations were performed for a lattice gas with up to fourth nearest neighbor interactions. These were chosen to reproduce the experimentally determined OW(110) phase diagram for θ ≤ 0.5 which shows a dominating p(2 × 1) phase around half coverage. It was found that the p(2 × 1) ordering strongly influences surface diffusion at low temperatures. The tracer diffusion coefficient shows a strong minimum slightly below half coverage and a very small maximum above half coverage. This behavior is attributed to the change of the dominating lattice defects of the p(2 × 1) phase from vacancies in filled rows below θ = 0.5 to interstitials in empty rows above θ = 0.5. For the p(2 × 1) ordered lattice gas phase the chemical diffusion coefficient exhibits a strong maximum which becomes more pronounced as the temperature is lowered. This is attributed to the behavior of mean square fluctuations 〈(δN)2〉〈N〉, i.e. the inverse of the thermodynamic factor, which dominates the chemical diffusion coefficient under these circumstances. The p(2 × 1) ordering causes the surface diffusion to become highly anisotropic. Attempts to simulate the increase in activation energy with coverage found experimentally showed that this was not possible without invoking adsorbate induced changes in the saddle point energies for diffusion.

Surface cosegregation and surface precipitation on Fe-3%V-C,N(100) single crystals

Abstract Surface cosegregation and surface precipitation has been studied on (100) oriented surfaces of Fe-3%V-C,N and Fe-3%V-C single crystals by means of AES and LEED. Between 450 and 750°C cosegregation leads to the formation of the two-dimensional surface compounds V(C,N) and VC, which are both epitaxially arranged on the substrate surface as indicated by LEED. The stoichiometry of the surface compounds, determined by quantitative evaluation of Auger spectra, is VC 1.2 and V(C x N y ). x + y = 1.2, the composition of the latter varies between V(C 0.6 N 0.6 ) at 450°C and V(C 0.2 N 1.0 ) at 650°C. Saturation is obse to 650°C, at higher temperatures the total surface coverage decreases gradually. Ar + sputtering and room temperature oxidation experiments indicate that the surface compounds form a homogeneous layer on the substrates, the layer thickness is estimated to be less than 2 atomic layers. Upon quenching V(C,N) and VC surface precipitates are growing on clean and sulphur saturated substrate surfaces to a thickness of the precipitates of about 50 A. Sulphur does not prevent the formation of surface precipitates upon quenching but effectively suppresses the formation of V(C,N) and VC surface compounds.

Diffusion of interacting lattice gases on heterogeneous surfaces with simple topographies

Collective diffusion coefficients are studied for heterogeneous bivariate trap surfaces with different topographies. The topography is shown to affect strongly the coverage dependence and Arrhenius behavior of diffusion coefficients. The fluctuation and Kubo-Green methods are in strong disagreement, which is attributed to the failure of the former when the probe size is of the order of the applicable scale length for the lattice gas.

Collective diffusion on strongly correlated heterogeneous surfaces

Abstract Collective diffusion coefficients are studied for heterogeneous bivariate surfaces with two different topographies, namely the random patches and the chessboard-like ordered distributions. The topography is shown to affect strongly the coverage dependence of the transport coefficients. Various diffusion quantities like the chemical D , jump D J and tracer D ∗ diffusion coefficients are analyzed by means of Monte Carlo simulations in the framework of the fluctuation and the Kubo–Green theory. The behavior of diffusion coefficients in small patches is mainly affected by the mobility of the particles in the border vacancies, and a simple law is obtained for the ratio D (1)/ D (0). For large patches the behavior is dominated by the mobility of particles in the central vacancies. In the limit of very large patches the diffusion coefficients become independent of the energetic topography.

Surface diffusion in the presence of phase transitions Monte Carlo studies of a simple lattice gas model

Abstract A comparison of the Kubo-Green and fluctuation methods for determining surface diffusion coefficients of adsorbates was carried out by Monte Carlo simulations on a square lattice for attractive nearest and repulsive next nearest neighbor interactions. Depending on R ≡ ϕ NNN ϕ NN the lattice gas models show first- and second-order phase transitions at low temperatures. In the presence of second-order phase transitions ( R = −2, R = −1) both methods agree, even in p(2 × 1) ordered regions of the relevant phase diagrams. For systems with first-order phase transitions ( R = −0.5, R = 0) we found a substantial remanent “graininess” of the lattice gas at temperatures well above T c . This graininess represents early stages of first-order phase transitions between lattice gas phases of substantially different particle density. It is shown for the first time that such remanent graininess affects the determination of the chemical surface diffusion coefficient, as diffusion measurements may depend to some extent on the length scale of the measuring technique.

Surface segregation phenomena on Fe3.5%MoN(100): the formation of a MoN surface compound

Abstract Molybdenum and nitrogen cosegregation is investigated on (100) oriented surfaces of Fe3.5%MoN single crystals applying Auger electron spectroscopy (AES) and low energy electron diffraction (LEED). The formation of a two-dimensional MoN surface compound occurs at temperatures ranging from 500 to 790°C. Ar + ion depth profiling indicates that the MoN consists of approximately two compound layers. Within the AES detection limit the existence of three-dimensional MoN surface precipitates is ruled out. The MoN-covered substrate surface exhibits a sharp (1 × 1) LEED pattern indicating the epitaxial stabilization of the MoN surface compound on the bcc (100) surface.

Effect of segregated antimony on the oxidation of Fe–4%Sb single crystals

Abstract Antimony surface segregation and its effect on oxidation were investigated on (111) and (110) oriented surfaces of Fe–4%Sb single crystals by means of AES (Auger Electron Spectroscopy) and LEED (Low Energy Electron Diffraction). Oxidation experiments were performed at 300°C and 500°C using oxygen pressures between 1×10 −8 mbar and 5×10 −6 mbar for both sputter cleaned surfaces and antimony saturated surfaces. The presence of antimony on the surface retards or even prevents oxidation for both surface orientations and at both temperatures under investigation. LEED patterns show complex superstructures as a result of oxidation of clean surfaces, while for the antimony saturated surfaces, no additional reflexes were detected at a similar degree of oxidation. Different possibilities to interpret the role of antimony in oxidation are discussed.

Surface segregation on Fe-25 %Cr-2 %Ni-0.14%Sb-N,S (100) single crystal surfaces

Abstract Surface segregation on (100) oriented single crystal surfaces of the alloy Fe–25%Cr–2%Ni–0.14%Sb–N,S has been investigated by means of Auger electron spectroscopy (AES), low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS). The experiments have been carried out in the temperature range from 500°C to 700°C in which a variety of segregation phenomena is observed. In the low temperature range, cosegregation of nitrogen and chromium occurs. Depth profiling and XPS studies suggest that the Cr and N segregation layer consists of (i) a two-dimensional surface compound and (ii) three-dimensional precipitates in the surface near region. A LEED investigation of the Cr and N saturated surface yields a clear (1×1) pattern after sufficiently long annealing times. At temperatures in excess of 600°C, segregated nitrogen and chromium are replaced by segregating antimony and nickel. Studies of the kinetics show that nickel and antimony jointly enrich at the sample surface; this proves that true cosegregation occurs. An XPS study of the antimony and nickel saturated surface shows that the antimony binding energy coincides with the value that had been measured for the binding energy of segregated antimony on pure iron. The corresponding LEED pattern shows reflex splitting which indicates domain formation. A further increase of the temperature to about 700°C causes segregation of sulphur displacing antimony from the surface. The sulphur covered surface exhibits a typical c(2×2) LEED pattern.