Kinetic Monte Carlo modeling of reaction-induced phase separation in Au/Ni(111) surface alloy
Introduction
Electronic, magnetic and catalytic properties of bimetallic systems on metal surfaces attract nowadays a considerable attention. Advances in surface growth technologies allow one to produce the so-called surface alloys which are formed only in the surface layer by two thermodynamically bulk-immiscible metals. Surface alloying by adatom exchange with surface atoms occurs [1], [2], [3], [4] at submonolayer coverage of adatom component.
In pursuit of a novel catalyst with improved properties in activity and selectivity working at industrial conditions, the Au–Ni surface alloy stability on Ni(111) was recently studied at high CO pressures [1]. However, a phase separation of Au and Ni components was observed, caused by gold-catalyzed Ni + CO reaction producing nickel carbonyl gas, Ni(CO)4, and facilitating nucleation of remaining Au into islands at the reaction front.
The Kinetic Monte Carlo (KMC) approach [5], [6], [7], [8] is a standard method used to model the microscopic details of such reaction-induced behavior. The KMC provides an advantage of studying activated, non-equilibrium processes in real time, while maintaining computational efficiency. However, a particular attention has to be paid to a reliable selection of diffusion, reaction and interaction parameters characterizing the dynamics of phase separation experiment [1]. For example, the range of diffusion rates might comprise many orders of magnitude: from very fast hopping (106 ÷ 107 s− 1) in the absence of nearest neighbor (NN) adatoms [9] to a complete immobility at kink sites, where a surface atom is attracted by, e.g., three NN adatoms [10]. Similarly, a large difference in magnitude of nickel carbonyl reaction (formation) rate for pure Ni foil [11] and Au/Ni(111) surface alloy [1] is observed being much higher for the alloy. In addition, the reaction rate could be modified by Au–CO and Ni–CO repulsion, which leads to reduction of CO in NN sites that are neighbors of both Ni and Au adatoms.
It should be noted that in the first computer simulations [8] reproducing the experiment [1] the role of CO was neglected, assuming that at high pressures all Au and Ni atoms are completely covered by CO molecules. By neglecting the CO-induced effects, it is impossible to simulate the experimentally observed step flow rate dependence on CO pressure (CO surface coverage, c). It also contradicts the X-ray diffraction study [12] indicating the existence of c = 0.57 phase and strong CO–CO repulsion on Ni(111) even at high CO pressures.
In this paper, we estimate parameters of pair- and three-body (trio) interactions between Au and Ni adatoms using ab initio calculations. Further, these interactions are used in the KMC simulation to model the reaction-induced phase separation in Au/Ni(111) surface alloy. We study the effect of trio interactions on qualitative (Au islands formation and purity, homogenous/inhomogeneous reaction flow) and quantitative (reaction delay, step flow rate) features of the reaction front propagation process. The rate and mechanism of front propagation are shown to be very sensitive to the values of interaction parameters, and at least three different reaction mechanisms can be predicted.
Section snippets
Calculation of interaction parameters
Calculations of formation energies of various ordered surface configurations were performed using ab initio Vienna simulation package (VASP) based on the density functional theory (DFT) [13]. The adsorbate structure was created on top and bottom of symmetrically terminated 5 Ni layer slab where the lower plane was a mirror plane of the upper plane. The positions of adatoms and all atoms in 5-layer slab were allowed to relax. The unit cell size periodicity varied from 1 × 1 to 4 × 4. A surface is
Microscopic model and KMC simulation parameters
We perform the simulation of reaction and phase separation process at room temperature (RT, T = 298 K) on a hexagonal lattice that mimics the fcc sites of Ni(111) surface. The periodic boundary conditions are implemented for left and right boundaries of the lattice, while top and bottom lines are free of boundary conditions. Unless specified otherwise, we set the width Lw/a = 90 and length Ll/a (up to 600) of the lattice, where a is the Ni(111) surface lattice constant. According to the experiment
KMC simulation of reaction propagation
Within the range of accuracy of VH and VI we observed two very different regimes of reaction front propagation and a third intermediate regime in-between. Though the range of VH and VI variation was rather small, the step flow rate in both main regimes could differ by an order of magnitude. The regimes were defined according to the following criteria:
- (a)
Step flow rate values (Fig. 2);
- (b)
Homogeneity of reaction process, since the formation of Au islands might occur as on reaction front as well as
Conclusions
The Au–Ni phase separation in Au/Ni(111) surface alloy during gold-catalyzed nickel carbonyl formation reaction was studied by means of the KMC simulations using realistic values of kinetic and interaction parameters. The ab initio calculations were performed to fit the nearest-neighbor pair- and trio- interaction potentials between Au and Ni adatoms. Also, the rates of Au and Ni diffusion, nickel carbonyl formation reaction and CO adsorption and desorption were taken into account using
Acknowledgments
Authors are greatly indebted to E.A. Kotomin for a number of stimulating discussions. G. Zvejnieks was financially supported by the Latvian Grant No. 237/2012. A. Ibenskas acknowledges funding support by European Union Structural Funds project “Postdoctoral Fellowship Implementation in Lithuania” (VP1-3.1-ŠMM-01-V-02-004).
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