Motion of small cross-channel clusters on W(2 1 1) surface: A density functional theory study
Introduction
To trigger modeling processes in nanoscale it is important to know energetics and mechanism involved in stability of objects on the surface. One from many important factors to understood is surface diffusion. It was already shown that a number of mechanisms could be involved in simple ad-atom motion [1]. The motion of clusters is obviously more complex. The number of open questions have to be addressed: Do clusters move as an entity or one ad-atom at the time? How the jumps are correlated? When we can treat motion of ad-atom as influenced only by the surface? Even for clusters composed of only two or three ad-atoms exist few possible configurations, and they determine the number of transitions which can occur. The transitions depend on surface structure, response of lattice, and energetics. In this paper we tackle the motion of dimers and trimers arranged on the channel W(2 1 1) surface in cross-channel fashion, always being separated at least one surface channel from other clusters. The arrangement like that was already investigated on W(2 1 1) experimentally for tungsten cross-channel doublets and triplets [2], rhenium doublets [3] and iridium doublets, triplets and tetramers [4]. In contrast to tungsten and rhenium cross-channel clusters, iridium clusters are always observed in the linear configuration, suggesting or concerted motion of clusters or much lower following jump with respect to limiting jump for the motion. The doublets on other channel surfaces were also subject of interest [5]. On some channel surfaces, as for example on Ir(1 1 0), it is required to consider exchange mechanism of motion [6], [7]. The exchange mechanism can be ruled out for W dimers on W(2 1 1) surface due to high energy of the process [5]. The W(2 1 1) can provide the template for an asymmetric motion. The asymmetric motion was not observed for motion of quasi-isolated ad-atoms on this plane [8], however the presence of ad-atom in adjacent channel might induce the asymmetry.
Properties of the cross-channel tungsten ad-dimers on W(2 1 1) surface and the energy barriers associated with the transition of such ad-dimer between its different configurations have been already considered in theoretical study based on the semi-empirical tight binding approach [9]. These results are at least partially in contradiction with existing experimental data. In Ref. [9] the staggered configuration is the energetically most optimal structure of the cross-channel ad-dimer with an energy 0.64 eV lower than for cross-channel ad-dimer in straight configuration. Additionally, the calculated energy barriers for the transition between these two configurations suggest that staggered configurations appear (on the timescale of experiment) at lower temperature than the straight configuration. This is in disagreement with experimental observations [2] of both staggered and straight cross-channel ad-dimers at 255 K.
Our study is based on the ab-initio calculations performed with the use of density functional theory (DFT) and plane wave basis set. We analyze, in detail, the structural, electronic and energetic properties of cross-channel tungsten ad-dimers and ad-trimers located at W(2 1 1) surface. The aim of this consideration is to clarify contradictions between results obtained from earlier theoretical work and experimental data provided by field ion microscopy measurements [5]. We have investigated the type and length of the interactions between tungsten ad-atoms moving in adjacent surface channels of W(2 1 1) substrate and their influence on the energy barriers associated with the jump of ad-atoms between subsequent adsorption sites. We have also considered two possible mechanisms of the motion of cross-channel ad-dimers and ad-trimers. We explored the spatial distribution of electronic charge and show the formation of the direct straight and staggered bonds. The results are analyzed and discussed in the context of existing theoretical and experimental data.
Section snippets
Computational details
The theoretical study has been performed with the use of ab-initio calculations based on DFT approach and the application of plane wave basis set, as implemented in Viena Ab-initio Simulation Package (VASP) code [10], [11], [12], [13]. The electron-ion interactions were described with the help of the projector-augmented wave (PAW) method. The description of the exchange-correlation effects was performed in the framework of the local density approximation (LDA). For the convergence of the energy
Adsorption of cross-channel ad-dimers
The cross-channel dimer can be observed in two types of configurations: straight and staggered. Both structures are shown schematically in Fig. 1a and b. The tungsten ad-atoms assembled in cross-channel straight dimer (cross1) are separated by 4.32 Å, the bond is 0.1 Å shorter than the cross-channel distance between adsorption places on the rigid surface. Both dimer's ad-atoms are shifted 0.05 Å towards each other, perpendicular to the rows and 0.09 Å in the direction (with respect to
Distance dependence of total energy and electronics
In Fig. 2a the shape and heights of the energy barriers associated with the movement of an ad-atom from cross-channel dimer during its jump out of straight configuration is presented. In Fig. 2b the sequence of spatial distributions of the electronic charge corresponding to the straight cross-channel ad-dimer (cross1) and other configurations representing the transition stages during the formation or dissociation of this ad-dimer is presented. These distributions are plotted in the plane
Diffusion of cross-channel dimer
The heights of the activation barriers for the transition between different configurations of our two-atomic systems are enclosed in Table 1. This data describes the energetics of the processes associated with the decomposition of the straight configurations (transitions from cross1 to cross4r and from cross1 to cross4l) as well as the association of ad-atoms into the straight cross-channel ad-dimer (transitions from cross4l to cross1 and from cross4r to cross1). In most cases calculations have
Adsorption of cross-channel trimers
We have investigated the structural, electronic and energetic properties of cross-channel ad-trimers in several configurations—all calculations were performed with the use of 4 × 5 unit cell. The most stable structure of the cross-channel ad-trimer is the straight configuration (tri1)—its geometrical properties are shown schematically in Fig. 5a. We have found that the outer ad-atoms of the ad-trimer are displaced 0.09 Å with respect to the adsorption sites of quasi-isolated ad-atoms, toward the
Diffusion of cross-channel trimers
We have analyzed the mechanism and the energy conditions for the jumps of the cross-channel ad-trimer in the straight configuration (most stable structure) to the next nearest equilibrium position (movement along the surface channels). Like in the case of cross-channel ad-dimer, we have considered here the surface diffusion mechanisms based on the concerted motion of the whole ad-trimer, and on the sequence of the separate jumps of particular ad-atoms (ad-atom by ad-atom motion). Fig. 7a
Summary
We have explored the motion of cross-channel dimers and trimers on W(2 1 1) plane. We found attractive interactions for both straight and staggered configurations. Such interactions are leading to shortening the bonds of cross-channel clusters (dimers and trimers). The most stable configurations are the straight configurations, but the staggered systems are energetically not much more demanding; only 0.01–0.03 eV higher. The attractive interactions lower the total energy of the system (∼0.20 eV),
Acknowledgments
GA would like thanks Prof. Gert Ehrlich for discussion. This work has been supported via research project No. 1010/S/IFD. Numerical calculations reported in this work have been performed at the Interdisciplinary Center for Mathematical and Computational Modeling of the University of Warsaw within Grant No. G44-10.
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