S Helfensteyn

Segregation and ordering at alloys surfaces: modelling and experiment confronted

Model calculations combining the Monte Carlo (MC) method and a suitable energy model are proposed as fully complementary to experiments in order to gain insight in segregation and other surface phenomena, deployed by materials in order to minimise their surface free energy and hence their total Gibbs free energy. In the confrontation between experiments and modelling, it is basically assumed that the surface, as observed in the experiments, corresponds to the equilibrium situation of minimal Gibbs free energy. The entropy part is modelled by the stochastic nature of Monte Carlo simulations, while the energy part is taken into account by the (modified) embedded atom method ((M)EAM). Special attention is paid to the derivation of model parameters that are specific for the alloy under study. For it appears that in several cases the experimental data can only correctly be reproduced with these specific EAM parameters. This article further focuses on the determination of the degree of order in the bulk. Simulations according to the Grand Canonical Ensemble require the difference in chemical potential between the components. A novel approach is presented for deriving this parameter both for slightly off-stoichiometric ordered alloys and for disordered alloys. Results of MC/(M)EAM simulations are presented for the surfaces of five catalytically important binary alloys: Au75Pd25(1 1 0), Cu75Pd25(1 1 0), Pt50Ni50(1 0 0), (1 1 0) and (1 1 1), Pt80Fe20(1 1 1) and Pt75Sn25(1 1 1). It can be concluded that these simulations yield excellent predictions for surface modifications and are a very powerful tool to model and understand surfaces at equilibrium. # 2003 Elsevier Science B.V. All rights reserved.

Preferential segregation to the step edges on Pt–Re catalyst particles

Abstract Monte Carlo simulations combined with the “macroscopic atom” model are used to investigate surface segregation in platinum–rhenium reforming catalysts. Two irregularly shaped particles of different size are implemented as an approximation to the active grains in commercial catalysts. Disordered configurations with bulk concentrations between 20 and 80 at.% Pt are studied. For all configurations segregation of Pt, the catalytically active element, is observed, up to 100 at.% Pt for the Pt-richer particles. The extent of segregation is in full agreement with the considerably lower surface tension of Pt and the negative enthalpy of solution in the Pt–Re system. It is furthermore less pronounced at higher temperatures, as it should be for exothermic segregation in disordered alloys. For the lowest concentrations the bulk is depleted upon segregation and this of course is more pronounced for the smaller particle. The interesting phenomenon that is observed is a strongly preferential segregation to the lattice sites with lowest coordination at the step edges. By systematically increasing the Pt-content of the particle the surface sites are sequentially filled in order of increasing coordination, in full agreement with thermodynamical considerations. This observation possibly points at steps and kinks as the active catalyst sites and is also in agreement with experimental evidence on Pt-surfaces [Surf. Sci. 128 (1983) 176] that showed a systematical increase in activity for rougher surfaces.

MAM modelling of the segregation and ordering at the Pt3Sn(111) surface

Abstract The temperature dependent segregation and ordering phenomena at the Pt 3 Sn(111) surface are modelled by means of Monte Carlo simulations combined with the “Macroscopic Atom” Model (MAM). The results are compared with experimental data by Ceelen et al. [W.C.A.N. Ceelen, A.W. Denier van der Gon, M.A. Reijme, H.H. Brongersma, I. Spolveri, A. Atrei, U. Bardi, Surf. Sci. 406 (1998) 264]. It appears from the simulations that the experimentally observed (√3×√3)R30° structure at 700 K in the increasing temperature trajectory is a consequence of two factors: a preferential sputtering in the cleaning procedure and a limited atomic mobility, at lower temperatures restricted to the two outermost layers. It is thus induced by the sample preparation and hence merely an artefact rather than an intrinsic property. Only for temperatures between 1000 and 1200 K is full equilibrium between surface and bulk reached. The endothermic Sn segregation and corresponding (2×2) order at these temperatures are also evidenced in the MAM calculations that are in good agreement with the experimental data.

ON THE CONSPICUOUS SEGREGATION BEHAVIOR AT Pt–Rh SURFACES

Phase demixing is evaluated as a possible explanation for the anomalous temperature dependence of the Pt segregation at the Pt50Rh50(511), Pt25Rh75(110) and Pt25Rh75(100) surfaces. Calculations are performed in the quasichemical approximation and a broken bond scheme. Although the calculations based on systematic demixing tend to overestimate the surface enrichment, the qualitative agreement appears to be rather good.

Synergy between material, surface science experiments and simulations

This chapter examines the link between bulk alloys and surfaces and the necessary conditions that effective simulation techniques must meet in order to properly describe, in a consistent manner, the varied phenomena that characterize each field of research. After a brief description of the thermodynamics of alloy formation and surface segregation in ordered and disordered alloys, model calculations combining the Monte Carlo method and suitable energy models are presented as fully complementary to experiments in order to gain insight in segregation and other surface phenomena, deployed by materials in order to minimize their surface free energy and hence their total Gibbs free energy. In the confrontation between experiments and modeling, it is assumed that the surface, as observed experimentally, corresponds to the equilibrium situation of minimal Gibbs free energy. The entropy part is modeled by the stochastic nature of Monte Carlo simulations, while the energy part is taken into account by appropriate energy models. In this chapter, we describe the (modified) embedded atom method, the derivation of its parameters, and its applications to several cases of interest.