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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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|
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\author{Joseph R. Michalka} |
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\author{Patrick W. McIntyre} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ University of Notre |
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Dame\\ Notre Dame, Indiana 46556} |
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|
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\keywords{} |
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|
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\begin{document} |
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|
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|
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%% |
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%Introduction |
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% Experimental observations |
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% Previous work on Pt, CO, etc. |
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% |
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%Simulation Methodology |
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% FF (fits and parameters) |
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% MD (setup, equilibration, collection) |
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% |
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% Analysis of trajectories!!! |
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%Discussion |
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% CO preferences for specific locales |
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% CO-CO interactions |
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% Differences between Au & Pt |
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% Causes of 2_layer reordering in Pt |
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%Summary |
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%% |
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|
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|
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\begin{abstract} |
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The mechanism and dynamics of surface reconstructions of Pt(557) and |
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Au(557) exposed to various coverages of carbon monoxide (CO) were |
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investigated using molecular dynamics simulations. Metal-CO |
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interactions were parameterized from experimental data and |
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plane-wave Density Functional Theory (DFT) calculations. The large |
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difference in binding strengths of the Pt-CO and Au-CO interactions |
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was found to play a significant role in step-edge stability and |
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adatom diffusion constants. Various mechanisms for CO-mediated step |
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wandering and step doubling were investigated on the Pt(557) |
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surface. We find that the energetics of CO adsorbed to the surface |
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can explain the step-doubling reconstruction observed on Pt(557) and |
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the lack of such a reconstruction on the Au(557) surface. However, |
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more complicated reconstructions into triangular clusters that have |
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been seen in recent experiments were not observed in these |
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simulations. |
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\end{abstract} |
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|
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\newpage |
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|
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|
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\section{Introduction} |
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% Importance: catalytically active metals are important |
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% Sub: Knowledge of how their surface structure affects their ability to catalytically facilitate certain reactions is growing, but is more reactionary than predictive |
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% Sub: Designing catalysis is the future, and will play an important role in numerous processes (ones that are currently seen to be impractical, or at least inefficient) |
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% Theory can explore temperatures and pressures which are difficult to work with in experiments |
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% Sub: Also, easier to observe what is going on and provide reasons and explanations |
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% |
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|
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Industrial catalysts usually consist of small particles that exhibit a |
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high concentration of steps, kink sites, and vacancies at the edges of |
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the facets. These sites are thought to be the locations of catalytic |
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activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now |
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significant evidence that solid surfaces are often structurally, |
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compositionally, and chemically modified by reactants under operating |
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conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between |
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surface oxidation states and catalytic activity for CO oxidation on |
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Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002} |
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Despite the well-documented role of these effects on reactivity, the |
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ability to capture or predict them in atomistic models is somewhat |
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limited. While these effects are perhaps unsurprising on the highly |
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disperse, multi-faceted nanoscale particles that characterize |
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industrial catalysts, they are manifest even on ordered, well-defined |
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surfaces. The Pt(557) surface, for example, exhibits substantial and |
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reversible restructuring under exposure to moderate pressures of |
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carbon monoxide.\cite{Tao:2010} |
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|
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This work is an investigation into the mechanism and timescale for the |
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Pt(557) \& Au(557) surface restructuring using molecular simulation. |
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Since the dynamics of the process are of particular interest, we |
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employ classical force fields that represent a compromise between |
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chemical accuracy and the computational efficiency necessary to |
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simulate the process of interest. Since restructuring typically |
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occurs as a result of specific interactions of the catalyst with |
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adsorbates, in this work, two metal systems exposed to carbon monoxide |
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were examined. The Pt(557) surface has already been shown to undergo a |
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large scale reconstruction under certain conditions.\cite{Tao:2010} |
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The Au(557) surface, because of weaker interactions with CO, is less |
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likely to undergo this kind of reconstruction. However, Peters {\it et |
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al}.\cite{Peters:2000} and Piccolo {\it et al}.\cite{Piccolo:2004} |
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have both observed CO-induced modification of reconstructions to the |
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Au(111) surface. Peters {\it et al}. observed the Au(111)-($22 \times |
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\sqrt{3}$) ``herringbone'' reconstruction relaxing slightly under CO |
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adsorption. They argued that only a few Au atoms become adatoms, |
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limiting the stress of this reconstruction, while allowing the rest to |
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relax and approach the ideal (111) configuration. Piccolo {\it et |
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al}. on the other hand, saw a more significant disruption of the |
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Au(111)-($22 \times \sqrt{3}$) herringbone pattern as CO adsorbed on |
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the surface. Both groups suggested that the preference CO shows for |
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low-coordinated Au atoms was the primary driving force for the |
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relaxation. Although the Au(111) reconstruction was not the primary |
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goal of our work, the classical models we have fit may be of future |
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use in simulating this reconstruction. |
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|
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%Platinum molecular dynamics |
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%gold molecular dynamics |
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|
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\section{Simulation Methods} |
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The challenge in modeling any solid/gas interface is the development |
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of a sufficiently general yet computationally tractable model of the |
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chemical interactions between the surface atoms and adsorbates. Since |
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the interfaces involved are quite large (10$^3$ - 10$^4$ atoms), have |
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many electrons, and respond slowly to perturbations, {\it ab initio} |
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molecular dynamics |
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(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
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methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
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mechanical potential energy surfaces remain out of reach. |
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Additionally, the ``bonds'' between metal atoms at a surface are |
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typically not well represented in terms of classical pairwise |
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interactions in the same way that bonds in a molecular material are, |
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nor are they captured by simple non-directional interactions like the |
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Coulomb potential. For this work, we have used classical molecular |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using |
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a rigid three-site model developed by Straub and Karplus for studying |
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photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
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Pt-CO cross interactions were parameterized as part of this work. |
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|
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\subsection{Metal-metal interactions} |
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Many of the potentials used for modeling transition metals are based |
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on a non-pairwise additive functional of the local electron |
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density. The embedded atom method (EAM) is perhaps the best known of |
151 |
these |
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methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
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but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
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the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
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parameter sets. The glue model of Ercolessi {\it et |
156 |
al}.\cite{Ercolessi88} is among the fastest of these density |
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functional approaches. In all of these models, atoms are treated as a |
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positively charged core with a radially-decaying valence electron |
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distribution. To calculate the energy for embedding the core at a |
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particular location, the electron density due to the valence electrons |
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at all of the other atomic sites is computed at atom $i$'s location, |
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\begin{equation*} |
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\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}) |
164 |
\end{equation*} |
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Here, $\rho_j(r_{ij})$ is the function that describes the distance |
166 |
dependence of the valence electron distribution of atom $j$. The |
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contribution to the potential that comes from placing atom $i$ at that |
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location is then |
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\begin{equation*} |
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V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
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\end{equation*} |
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where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
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$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
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repulsive overlap of the two positively charged cores. |
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|
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% The {\it modified} embedded atom method (MEAM) adds angular terms to |
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% the electron density functions and an angular screening factor to the |
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% pairwise interaction between two |
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% atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve} |
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% MEAM has become widely used to simulate systems in which angular |
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% interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc |
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% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
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% MEAM presents significant additional computational costs, however. |
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|
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The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
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have all been widely used by the materials simulation community for |
187 |
simulations of bulk and nanoparticle |
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properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq,mishin99:_inter} |
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melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr} |
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fracture,\cite{Shastry:1996qg,Shastry:1998dx,mishin01:cu} crack |
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propagation,\cite{BECQUART:1993rg,Rifkin1992} and alloying |
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dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
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One of EAM's strengths is its sensitivity to small changes in |
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structure. This is due to the inclusion of up to the third nearest |
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neighbor interactions during fitting of the parameters.\cite{Voter95a} |
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In comparison, the glue model of Ercolessi {\it et |
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al}.\cite{Ercolessi88} was only parameterized to include |
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nearest-neighbor interactions, EAM is a suitable choice for systems |
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where the bulk properties are of secondary importance to low-index |
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surface structures. Additionally, the similarity of EAM's functional |
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treatment of the embedding energy to standard density functional |
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theory (DFT) makes fitting DFT-derived cross potentials with |
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adsorbates somewhat easier. |
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|
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\subsection{Carbon Monoxide model} |
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Previous explanations for the surface rearrangements center on the |
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large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} We |
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used a model first proposed by Karplus and Straub to study the |
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photodissociation of CO from myoglobin because it reproduces the |
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quadrupole moment well.\cite{Straub} The Straub and Karplus model |
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treats CO as a rigid three site molecule with a massless |
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charge-carrying ``M'' site at the center of mass. The geometry and |
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interaction parameters are reproduced in Table~\ref{tab:CO}. The |
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effective dipole moment, calculated from the assigned charges, is |
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still small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is |
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close to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
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mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
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%CO Table |
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\begin{table}[H] |
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\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
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$\epsilon$), and charges for CO-CO |
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interactions. Distances are in \AA, energies are |
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in kcal/mol, and charges are in atomic units. The CO model |
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from Ref.\bibpunct{}{}{,}{n}{}{,} |
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\protect\cite{Straub} was used without modification.} |
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\centering |
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\begin{tabular}{| c | c | ccc |} |
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\hline |
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& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
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\hline |
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\textbf{C} & -0.6457 & 3.83 & 0.0262 & -0.75 \\ |
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\textbf{O} & 0.4843 & 3.12 & 0.1591 & -0.85 \\ |
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\textbf{M} & 0.0 & - & - & 1.6 \\ |
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\hline |
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\end{tabular} |
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\label{tab:CO} |
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\end{table} |
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|
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\subsection{Cross-Interactions between the metals and carbon monoxide} |
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|
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Since the adsorption of CO onto a Pt surface has been the focus |
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of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
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and theoretical work |
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\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
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there is a significant amount of data on adsorption energies for CO on |
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clean metal surfaces. An earlier model by Korzeniewski {\it et |
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al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
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modified to ensure that the Pt-CO interaction favored the atop binding |
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position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
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The modified parameters yield binding energies that are slightly higher |
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than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
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{\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
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Lennard-Jones interaction to mimic strong, but short-ranged, partial |
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binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
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Pt-O interaction was modeled with a Morse potential with a large |
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equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
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over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak |
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repulsion which favors the atop site. The resulting potential-energy |
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surface suitably recovers the calculated Pt-C separation length |
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(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
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position.\cite{Deshlahra:2012, Hopster:1978} |
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|
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%where did you actually get the functionals for citation? |
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%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
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%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
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The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
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Morse potentials, respectively, to reproduce Au-CO binding energies. |
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The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
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Adsorption energies were obtained from gas-surface DFT calculations with a |
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periodic supercell plane-wave basis approach, as implemented in the |
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Quantum ESPRESSO package.\cite{QE-2009} Electron cores were |
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described with the projector augmented-wave (PAW) |
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method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
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included to an energy cutoff of 20 Ry. Electronic energies are |
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computed with the PBE implementation of the generalized gradient |
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approximation (GGA) for gold, carbon, and oxygen that was constructed |
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by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
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In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
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Au x 2 Au surface planes and separated from vertical images by six |
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layers of vacuum space. The surface atoms were all allowed to relax |
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before CO was added to the system. Electronic relaxations were |
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performed until the energy difference between subsequent steps |
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was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
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were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
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zone.\cite{Monkhorst:1976} The relaxed gold slab was |
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then used in numerous single point calculations with CO at various |
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heights (and angles relative to the surface) to allow fitting of the |
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empirical force field. |
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|
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%Hint at future work |
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The parameters employed for the metal-CO cross-interactions in this work |
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are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
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(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
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and polarization are neglected in this model, although these effects could have |
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an effect on binding energies and binding site preferences. |
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|
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%Table of Parameters |
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%Pt Parameter Set 9 |
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%Au Parameter Set 35 |
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\begin{table}[H] |
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\caption{Parameters for the metal-CO cross-interactions. Metal-C |
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interactions are modeled with Lennard-Jones potentials, while the |
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metal-O interactions were fit to broad Morse |
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potentials. Distances are given in \AA~and energies in kcal/mol. } |
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\centering |
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\begin{tabular}{| c | cc | c | ccc |} |
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\hline |
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& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\ |
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\hline |
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\textbf{Pt-C} & 1.3 & 15 & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\ |
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\textbf{Au-C} & 1.9 & 6.5 & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\ |
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|
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\hline |
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\end{tabular} |
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\label{tab:co_parameters} |
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\end{table} |
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|
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%Table of energies |
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\begin{table}[H] |
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\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
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described in this work. All values are in eV.} |
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\centering |
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\begin{tabular}{| c | cc |} |
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\hline |
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& Calculated & Experimental \\ |
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\hline |
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\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.81} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
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(Ref. \protect\cite{Kelemen:1979}) \\ |
329 |
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
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\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
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\hline |
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\end{tabular} |
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\label{tab:co_energies} |
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\end{table} |
335 |
|
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|
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\subsection{Force field validation} |
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The CO-Pt cross interactions were compared directly to DFT results |
339 |
found in the supporting information of reference |
340 |
{\bibpunct{}{}{,}{n}{}{,} \protect\cite{Tao:2010}}. These energies are |
341 |
estimates of the degree of stabilization provided to double-layer |
342 |
reconstructions of the M(557) surface by an overlayer of CO molecules |
343 |
in a $c (2 \times 4)$ pattern. To make the comparison, five atom |
344 |
thick metal slabs of both Pt and Au displaying the (557) facet were |
345 |
constructed. Double-layer (reconstructed) systems were created using |
346 |
six atomic layers where enough of a layer was removed from both |
347 |
exposed (557) facets to create the double step. In all cases, the |
348 |
metal slabs contained 480 atoms and were minimized using steepest |
349 |
descent under the EAM force field. Both the bare metal slabs and slabs |
350 |
with 50\% carbon monoxide coverage (arranged in the $c (2 \times 4)$ |
351 |
pattern) were used. The systems are periodic along and perpendicular |
352 |
to the step-edge axes with a large vacuum above the displayed (557) |
353 |
facet. |
354 |
|
355 |
Energies computed using our force field are displayed in Table |
356 |
~\ref{tab:steps}. The relative energies are calculated as |
357 |
$E_{relative} = E_{system} - E_{M(557)-S} - N_{CO}*E_{M-CO}(r)$, where |
358 |
$E_{M(557)-S}$ is the energy of a clean (557) surface. $N_{CO}$ is the |
359 |
number of CO molecules present on the surface. In the $c (2 \times |
360 |
4)$ patterning, the CO molecules relax to an average separation, $r$, |
361 |
from the nearest surface metal atom. $E_{M-CO}(r)$ is taken as the |
362 |
energy of a single CO molecule on a flat M(111) surface at a distance |
363 |
$r$ from a metal atop site. These energies correspond to -1.8 eV for |
364 |
CO-Pt and -0.39 eV for CO-Au. |
365 |
|
366 |
One important note is that the $c (2 \times 4)$ patterning on the |
367 |
stepped surfaces yields a slightly larger M-CO separation than one |
368 |
would find on a clean (111) surface. On a clean Pt(111) surface, for |
369 |
example, the optimized geometry has a C-Pt distance of 1.53~\AA |
370 |
(corresponding to a binding energy of -1.83 eV). On the double-layer |
371 |
reconstruction and the single (557) step, the half monolayer optimizes |
372 |
to C-Pt separations of 1.58-1.60~\AA, respectively. Although this |
373 |
difference seems quite small, there are notable consequences for |
374 |
$E_{Pt-CO}(r)$ which then takes values from -1.815 eV to -1.8 eV. |
375 |
|
376 |
For platinum, the bare double layer reconstruction is less stable than |
377 |
the bare (557) step by about 0.25 kcal/mol per Pt atom. However, |
378 |
addition of carbon monoxide changes the relative energetics of the two |
379 |
systems. This is a quite dramatic shift, $\Delta\Delta E$ (the change |
380 |
in energy for going from single to double-layer structures upon |
381 |
addition of a CO layer) shifts by -0.5~kcal/mol per Pt atom. This |
382 |
result is in qualitative agreement with the DFT calculations in |
383 |
reference {\bibpunct{}{}{,}{n}{}{,} \protect\cite{Tao:2010}}, which |
384 |
also showed that the addition of CO leads to a reversal in stability. |
385 |
|
386 |
The gold systems show a smaller energy difference between the clean |
387 |
single and double layers. Upon addition of CO, the single step surface |
388 |
is much more stable than the double-layer reconstruction. However, |
389 |
the CO-Au binding energy is much weaker, so at operating temperatures, |
390 |
the actual coverage by CO will be much lower than the 50\% coverage |
391 |
afforded by the $c (2 \times 4)$ pattern, so single-point energy |
392 |
comparisons are not as helpful. |
393 |
|
394 |
%Table of single step double step calculations |
395 |
\begin{table}[H] |
396 |
\caption{Relative energies (in kcal/mol) of (S)ingle M(557) and |
397 |
(D)ouble-step reconstructions. 50\% coverage by CO in a $c(2 |
398 |
\times 4)$ pattern stabilizes the D-reconstructed Pt(557) |
399 |
surface, but leaves the single-step Au(557) as the more stable structure.} |
400 |
\centering |
401 |
\begin{tabular}{| c | c | c | c | c |} |
402 |
\hline |
403 |
Step & $N_{M}$ & $N_{CO}$ & Relative Energy & $\Delta E / N_{M}$ \\ |
404 |
\hline |
405 |
Pt(557)-S & 480 & 0 & 0 & 0 \\ |
406 |
Pt(557)-D & 480 & 0 & 119.788 & 0.2495 \\ |
407 |
Pt(557)-S & 480 & 40 & -109.734 & -0.2286 \\ |
408 |
Pt(557)-D & 480 & 48 & -110.039 & -0.2292 \\ |
409 |
\hline |
410 |
\hline |
411 |
Au(557)-S & 480 & 0 & 0 & 0 \\ |
412 |
Au(557)-D & 480 & 0 & 83.853 & 0.1747 \\ |
413 |
Au(557)-S & 480 & 40 & -253.604 & -0.5283 \\ |
414 |
Au(557)-D & 480 & 48 & -156.150 & -0.3253 \\ |
415 |
\hline |
416 |
\end{tabular} |
417 |
\label{tab:steps} |
418 |
\end{table} |
419 |
|
420 |
Qualitatively, our classical force field for the metal-CO cross |
421 |
interactions reproduces the results predicted by DFT studies in |
422 |
reference {\bibpunct{}{}{,}{n}{}{,} \protect\cite{Tao:2010}}. Addition |
423 |
of polarization effects, both in the CO and in the metal surfaces, |
424 |
could make the model significantly more accurate. For example, |
425 |
because of the relatively large fixed charges, the current model will |
426 |
be unable to reproduce coverages in excess of 50\% without forming an |
427 |
inverted CO second layer on the surface. The M-CO cross interactions |
428 |
would also be more accurate if they included the direct interactions |
429 |
between charges on the CO and their image charges inside the metal |
430 |
slab. These polarization effects have been shown to play an important |
431 |
role,\cite{Deshlahra:2012} and would be one way of improving the |
432 |
numerical agreement with quantum mechanical calculations. |
433 |
|
434 |
\subsection{Pt(557) and Au(557) metal interfaces} |
435 |
Our Pt system is an orthorhombic periodic box of dimensions |
436 |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
437 |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
438 |
are 9 and 8 atoms deep respectively, corresponding to a slab |
439 |
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
440 |
The systems are arranged in a FCC crystal that have been cut |
441 |
along the (557) plane so that they are periodic in the {\it x} and |
442 |
{\it y} directions, and have been oriented to expose two aligned |
443 |
(557) cuts along the extended {\it z}-axis. Simulations of the |
444 |
bare metal interfaces at temperatures ranging from 300~K to |
445 |
1200~K were performed to confirm the relative |
446 |
stability of the surfaces without a CO overlayer. |
447 |
|
448 |
The different bulk melting temperatures predicted by EAM |
449 |
(1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for |
450 |
Pt\cite{Pt:melting}) suggest that any reconstructions should happen at |
451 |
different temperatures for the two metals. The bare Au and Pt |
452 |
surfaces were initially run in the canonical (NVT) ensemble at 800~K |
453 |
and 1000~K respectively for 100 ps. The two surfaces were relatively |
454 |
stable at these temperatures when no CO was present, but experienced |
455 |
increased surface mobility on addition of CO. Each surface was then |
456 |
dosed with different concentrations of CO that was initially placed in |
457 |
the vacuum region. Upon full adsorption, these concentrations |
458 |
correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher |
459 |
coverages resulted in the formation of a double layer of CO, which |
460 |
introduces artifacts that are not relevant to (557) reconstruction. |
461 |
Because of the difference in binding energies, nearly all of the CO |
462 |
was bound to the Pt surface, while the Au surfaces often had a |
463 |
significant CO population in the gas phase. These systems were |
464 |
allowed to reach thermal equilibrium (over 5~ns) before being run in |
465 |
the microcanonical (NVE) ensemble for data collection. All of the |
466 |
systems examined had at least 40~ns in the data collection stage, |
467 |
although simulation times for some Pt of the systems exceeded 200~ns. |
468 |
Simulations were carried out using the open source molecular dynamics |
469 |
package, OpenMD.\cite{Ewald,OOPSE,openmd} |
470 |
|
471 |
|
472 |
% RESULTS |
473 |
% |
474 |
\section{Results} |
475 |
\subsection{Structural remodeling} |
476 |
The bare metal surfaces experienced minor roughening of the step-edge |
477 |
because of the elevated temperatures, but the (557) face was stable |
478 |
throughout the simulations. The surfaces of both systems, upon dosage |
479 |
of CO, began to undergo extensive remodeling that was not observed in |
480 |
the bare systems. Reconstructions of the Au systems were limited to |
481 |
breakup of the step-edges and some step wandering. The lower coverage |
482 |
Pt systems experienced similar step edge wandering but to a greater |
483 |
extent. The 50\% coverage Pt system was unique among our simulations |
484 |
in that it formed well-defined and stable double layers through step |
485 |
coalescence, similar to results reported by Tao {\it et |
486 |
al}.\cite{Tao:2010} |
487 |
|
488 |
\subsubsection{Step wandering} |
489 |
The bare surfaces for both metals showed minimal step-wandering at |
490 |
their respective temperatures. As the CO coverage increased however, |
491 |
the mobility of the surface atoms, described through adatom diffusion |
492 |
and step-edge wandering, also increased. Except for the 50\% Pt |
493 |
system where step coalescence occurred, the step-edges in the other |
494 |
simulations preferred to keep nearly the same distance between steps |
495 |
as in the original (557) lattice, $\sim$13\AA~for Pt and |
496 |
$\sim$14\AA~for Au. Previous work by Williams {\it et |
497 |
al}.\cite{Williams:1991, Williams:1994} highlights the repulsion |
498 |
that exists between step-edges even when no direct interactions are |
499 |
present in the system. This repulsion is caused by an entropic barrier |
500 |
that arises from the fact that steps cannot cross over one |
501 |
another. This entropic repulsion does not completely define the |
502 |
interactions between steps, however, so it is possible to observe step |
503 |
coalescence on some surfaces.\cite{Williams:1991} The presence and |
504 |
concentration of adsorbates, as shown in this work, can affect |
505 |
step-step interactions, potentially leading to a new surface structure |
506 |
as the thermodynamic equilibrium. |
507 |
|
508 |
\subsubsection{Double layers} |
509 |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the |
510 |
Pt(557) surface undergoes two separate reconstructions upon CO |
511 |
adsorption. The first involves a doubling of the step height and |
512 |
plateau length. Similar behavior has been seen on a number of |
513 |
surfaces at varying conditions, including Ni(977) and |
514 |
Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we |
515 |
examined, the Pt system showed a greater propensity for reconstruction |
516 |
because of the larger surface mobility and the greater extent of step |
517 |
wandering. The amount of reconstruction was strongly correlated to |
518 |
the amount of CO adsorbed upon the surface. This appears to be |
519 |
related to the effect that adsorbate coverage has on edge breakup and |
520 |
on the surface diffusion of metal adatoms. Only the 50\% Pt surface |
521 |
underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within |
522 |
the time scales studied here. Over a longer time scale (150~ns) two |
523 |
more double layers formed on this surface. Although double layer |
524 |
formation did not occur in the other Pt systems, they exhibited more |
525 |
step-wandering and roughening compared to their Au counterparts. The |
526 |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
527 |
various times along the simulation showing the evolution of a double |
528 |
layer step-edge. |
529 |
|
530 |
The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010} |
531 |
involved the formation of triangular clusters that stretched across |
532 |
the plateau between two step-edges. Neither of the simulated metal |
533 |
interfaces, within the 40~ns time scale or the extended time of 150~ns |
534 |
for the 50\% Pt system, experienced this reconstruction. |
535 |
|
536 |
%Evolution of surface |
537 |
\begin{figure}[H] |
538 |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} |
539 |
\caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a) |
540 |
258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after |
541 |
exposure. Disruption of the (557) step-edges occurs quickly. The |
542 |
doubling of the layers appears only after two adjacent step-edges |
543 |
touch. The circled spot in (b) nucleated the growth of the double |
544 |
step observed in the later configurations.} |
545 |
\label{fig:reconstruct} |
546 |
\end{figure} |
547 |
|
548 |
\subsection{Dynamics} |
549 |
Previous experimental work by Pearl and Sibener\cite{Pearl}, using |
550 |
STM, has been able to capture the coalescence of steps on Ni(977). The |
551 |
time scale of the image acquisition, $\sim$70~s/image, provides an |
552 |
upper bound for the time required for the doubling to occur. By |
553 |
utilizing Molecular Dynamics we are able to probe the dynamics of |
554 |
these reconstructions at elevated temperatures and in this section we |
555 |
provide data on the timescales for transport properties, |
556 |
e.g. diffusion and layer formation time. |
557 |
|
558 |
|
559 |
\subsubsection{Transport of surface metal atoms} |
560 |
%forcedSystems/stepSeparation |
561 |
|
562 |
The wandering of a step-edge is a cooperative effect arising from the |
563 |
individual movements of the atoms making up the steps. An ideal metal |
564 |
surface displaying a low index facet, (111) or (100), is unlikely to |
565 |
experience much surface diffusion because of the large energetic |
566 |
barrier that must be overcome to lift an atom out of the surface. The |
567 |
presence of step-edges and other surface features on higher-index |
568 |
facets provides a lower energy source for mobile metal atoms. Using |
569 |
our potential model, single-atom break-away from a step-edge on a |
570 |
clean surface still imposes an energetic penalty around |
571 |
$\sim$~45~kcal/mol, but this is certainly easier than lifting the same |
572 |
metal atom vertically out of the surface, \textgreater~60~kcal/mol. |
573 |
The penalty lowers significantly when CO is present in sufficient |
574 |
quantities on the surface. For certain distributions of CO, the |
575 |
energetic penalty can fall to as low as $\sim$~20~kcal/mol. The |
576 |
configurations that create these lower barriers are detailed in the |
577 |
discussion section below. |
578 |
|
579 |
Once an adatom exists on the surface, the barrier for diffusion is |
580 |
negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are |
581 |
then able to explore the terrace before rejoining either their |
582 |
original step-edge or becoming a part of a different edge. It is an |
583 |
energetically unfavorable process with a high barrier for an atom to |
584 |
traverse to a separate terrace although the presence of CO can lower |
585 |
the energy barrier required to lift or lower an adatom. By tracking |
586 |
the mobility of individual metal atoms on the Pt and Au surfaces we |
587 |
were able to determine the relative diffusion constants, as well as |
588 |
how varying coverages of CO affect the diffusion. Close observation of |
589 |
the mobile metal atoms showed that they were typically in equilibrium |
590 |
with the step-edges. At times, their motion was concerted, and two or |
591 |
more adatoms would be observed moving together across the surfaces. |
592 |
|
593 |
A particle was considered ``mobile'' once it had traveled more than |
594 |
2~\AA~ between saved configurations of the system (typically 10-100 |
595 |
ps). A mobile atom would typically travel much greater distances than |
596 |
this, but the 2~\AA~cutoff was used to prevent swamping the diffusion |
597 |
data with the in-place vibrational movement of buried atoms. Diffusion |
598 |
on a surface is strongly affected by local structures and the presence |
599 |
of single and double layer step-edges causes the diffusion parallel to |
600 |
the step-edges to be larger than the diffusion perpendicular to these |
601 |
edges. Parallel and perpendicular diffusion constants are shown in |
602 |
Figure \ref{fig:diff}. Diffusion parallel to the step-edge is higher |
603 |
than diffusion perpendicular to the edge because of the lower energy |
604 |
barrier associated with sliding along an edge compared to breaking |
605 |
away to form an isolated adatom. |
606 |
|
607 |
%Diffusion graph |
608 |
\begin{figure}[H] |
609 |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1} |
610 |
\caption{Diffusion constants for mobile surface atoms along directions |
611 |
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
612 |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
613 |
surface coverage. The two reported diffusion constants for the 50\% |
614 |
Pt system correspond to a 20~ns period before the formation of the |
615 |
double layer (upper points), and to the full 40~ns sampling period |
616 |
(lower points).} |
617 |
\label{fig:diff} |
618 |
\end{figure} |
619 |
|
620 |
The weaker Au-CO interaction is evident in the weak CO-coverage |
621 |
dependance of Au diffusion. This weak interaction leads to lower |
622 |
observed coverages when compared to dosage amounts. This further |
623 |
limits the effect the CO can have on surface diffusion. The correlation |
624 |
between coverage and Pt diffusion rates shows a near linear relationship |
625 |
at the earliest times in the simulations. Following double layer formation, |
626 |
however, there is a precipitous drop in adatom diffusion. As the double |
627 |
layer forms, many atoms that had been tracked for mobility data have |
628 |
now been buried, resulting in a smaller reported diffusion constant. A |
629 |
secondary effect of higher coverages is CO-CO cross interactions that |
630 |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
631 |
This effect would become evident only at higher coverages. A detailed |
632 |
account of Pt adatom energetics follows in the Discussion. |
633 |
|
634 |
\subsubsection{Dynamics of double layer formation} |
635 |
The increased diffusion on Pt at the higher CO coverages is the primary |
636 |
contributor to double layer formation. However, this is not a complete |
637 |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
638 |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
639 |
system, one double layer formed within the first 40~ns of simulation time, |
640 |
while two more were formed as the system was allowed to run for an |
641 |
additional 110~ns (150~ns total). This suggests that this reconstruction |
642 |
is a rapid process and that the previously mentioned upper bound is a |
643 |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
644 |
appearance of a double layer appears at 19~ns into the simulation. |
645 |
Within 12~ns of this nucleation event, nearly half of the step has formed |
646 |
the double layer and by 86~ns the complete layer has flattened out. |
647 |
From the appearance of the first nucleation event to the first observed |
648 |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
649 |
necessary for the layer to completely straighten. The other two layers in |
650 |
this simulation formed over periods of 22~ns and 42~ns respectively. |
651 |
A possible explanation for this rapid reconstruction is the elevated |
652 |
temperatures under which our systems were simulated. The process |
653 |
would almost certainly take longer at lower temperatures. Additionally, |
654 |
our measured times for completion of the doubling after the appearance |
655 |
of a nucleation site are likely affected by our periodic boxes. A longer |
656 |
step-edge will likely take longer to ``zipper''. |
657 |
|
658 |
|
659 |
%Discussion |
660 |
\section{Discussion} |
661 |
We have shown that a classical potential is able to model the initial |
662 |
reconstruction of the Pt(557) surface upon CO adsorption, and have |
663 |
reproduced the double layer structure observed by Tao {\it et |
664 |
al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be |
665 |
rapid -- occurring within 100 ns of the initial exposure to CO. Here |
666 |
we discuss the features of the classical potential that are |
667 |
contributing to the stability and speed of the Pt(557) reconstruction. |
668 |
|
669 |
\subsection{Diffusion} |
670 |
The perpendicular diffusion constant appears to be the most important |
671 |
indicator of double layer formation. As highlighted in Figure |
672 |
\ref{fig:reconstruct}, the formation of the double layer did not begin |
673 |
until a nucleation site appeared. Williams {\it et |
674 |
al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge |
675 |
repulsion arising from the inability of edge crossing. This repulsion |
676 |
must be overcome to allow step coalescence. A larger |
677 |
$\textbf{D}_\perp$ value implies more step-wandering and a larger |
678 |
chance for the stochastic meeting of two edges to create a nucleation |
679 |
point. Diffusion parallel to the step-edge can help ``zipper'' up a |
680 |
nascent double layer. This helps explain the rapid time scale for |
681 |
double layer completion after the appearance of a nucleation site, while |
682 |
the initial appearance of the nucleation site was unpredictable. |
683 |
|
684 |
\subsection{Mechanism for restructuring} |
685 |
Since the Au surface showed no large scale restructuring in any of our |
686 |
simulations, our discussion will focus on the 50\% Pt-CO system which |
687 |
did exhibit doubling. A number of possible mechanisms exist to explain |
688 |
the role of adsorbed CO in restructuring the Pt surface. Quadrupolar |
689 |
repulsion between adjacent CO molecules adsorbed on the surface is one |
690 |
possibility. However, the quadrupole-quadrupole interaction is |
691 |
short-ranged and is attractive for some orientations. If the CO |
692 |
molecules are ``locked'' in a vertical orientation, through atop |
693 |
adsorption for example, this explanation would gain credence. Within |
694 |
the framework of our classical potential, the calculated energetic |
695 |
repulsion between two CO molecules located a distance of |
696 |
2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a |
697 |
vertical orientation, is 8.62 kcal/mol. Moving the CO to the second |
698 |
nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly |
699 |
0. Allowing the CO to rotate away from a purely vertical orientation |
700 |
also lowers the repulsion. When the carbons are locked at a distance |
701 |
of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle |
702 |
between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
703 |
barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
704 |
repulsion between adjacent CO molecules bound to Pt could indeed |
705 |
increase the surface diffusion. However, the residence time of CO on |
706 |
Pt suggests that the CO molecules are extremely mobile, with diffusion |
707 |
constants 40 to 2500 times larger than surface Pt atoms. This mobility |
708 |
suggests that the CO molecules jump between different Pt atoms |
709 |
throughout the simulation. However, they do stay bound to individual |
710 |
Pt atoms for long enough to modify the local energy landscape for the |
711 |
mobile adatoms. |
712 |
|
713 |
A different interpretation of the above mechanism which takes the |
714 |
large mobility of the CO into account, would be in the destabilization |
715 |
of Pt-Pt interactions due to bound CO. Destabilizing Pt-Pt bonds at |
716 |
the edges could lead to increased step-edge breakup and diffusion. On |
717 |
the bare Pt(557) surface the barrier to completely detach an edge atom |
718 |
is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
719 |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain |
720 |
configurations, cases (e), (g), and (h), the barrier can be lowered to |
721 |
$\sim$23~kcal/mol by the presence of bound CO molecules. In these |
722 |
instances, it becomes energetically favorable to roughen the edge by |
723 |
introducing a small separation of 0.5 to 1.0~\AA. This roughening |
724 |
becomes immediately obvious in simulations with significant CO |
725 |
populations. The roughening is present to a lesser extent on surfaces |
726 |
with lower CO coverage (and even on the bare surfaces), although in |
727 |
these cases it is likely due to random fluctuations that squeeze out |
728 |
step-edge atoms. Step-edge breakup by direct single-atom translations |
729 |
(as suggested by these energy curves) is probably a worst-case |
730 |
scenario. Multistep mechanisms in which an adatom moves laterally on |
731 |
the surface after being ejected would be more energetically favorable. |
732 |
This would leave the adatom alongside the ledge, providing it with |
733 |
five nearest neighbors. While fewer than the seven neighbors it had |
734 |
as part of the step-edge, it keeps more Pt neighbors than the three |
735 |
neighbors an isolated adatom has on the terrace. In this proposed |
736 |
mechanism, the CO quadrupolar repulsion still plays a role in the |
737 |
initial roughening of the step-edge, but not in any long-term bonds |
738 |
with individual Pt atoms. Higher CO coverages create more |
739 |
opportunities for the crowded CO configurations shown in Figure |
740 |
\ref{fig:SketchGraphic}, and this is likely to cause an increased |
741 |
propensity for step-edge breakup. |
742 |
|
743 |
%Sketch graphic of different configurations |
744 |
\begin{figure}[H] |
745 |
\includegraphics[width=\linewidth]{COpaths} |
746 |
\caption{Configurations used to investigate the mechanism of step-edge |
747 |
breakup on Pt(557). In each case, the central (starred) atom was |
748 |
pulled directly across the surface away from the step edge. The Pt |
749 |
atoms on the upper terrace are colored dark grey, while those on the |
750 |
lower terrace are in white. In each of these configurations, some |
751 |
of the atoms (highlighted in blue) had CO molecules bound in the |
752 |
vertical atop position. The energies of these configurations as a |
753 |
function of central atom displacement are displayed in Figure |
754 |
\ref{fig:SketchEnergies}.} |
755 |
\label{fig:SketchGraphic} |
756 |
\end{figure} |
757 |
|
758 |
%energy graph corresponding to sketch graphic |
759 |
\begin{figure}[H] |
760 |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison} |
761 |
\caption{Energies for displacing a single edge atom perpendicular to |
762 |
the step edge as a function of atomic displacement. Each of the |
763 |
energy curves corresponds to one of the labeled configurations in |
764 |
Figure \ref{fig:SketchGraphic}, and the energies are referenced to |
765 |
the unperturbed step-edge. Certain arrangements of bound CO |
766 |
(notably configurations g and h) can lower the energetic barrier for |
767 |
creating an adatom relative to the bare surface (configuration a).} |
768 |
\label{fig:SketchEnergies} |
769 |
\end{figure} |
770 |
|
771 |
While configurations of CO on the surface are able to increase |
772 |
diffusion and the likelihood of edge wandering, this does not provide |
773 |
a complete explanation for the formation of double layers. If adatoms |
774 |
were constrained to their original terraces then doubling could not |
775 |
occur. A mechanism for vertical displacement of adatoms at the |
776 |
step-edge is required to explain the doubling. |
777 |
|
778 |
We have discovered one possible mechanism for a CO-mediated vertical |
779 |
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} |
780 |
shows four points along a reaction coordinate in which a CO-bound |
781 |
adatom along the step-edge ``burrows'' into the edge and displaces the |
782 |
original edge atom onto the higher terrace. A number of events |
783 |
similar to this mechanism were observed during the simulations. We |
784 |
predict an energetic barrier of 20~kcal/mol for this process (in which |
785 |
the displaced edge atom follows a curvilinear path into an adjacent |
786 |
3-fold hollow site). The barrier heights we obtain for this reaction |
787 |
coordinate are approximate because the exact path is unknown, but the |
788 |
calculated energy barriers would be easily accessible at operating |
789 |
conditions. Additionally, this mechanism is exothermic, with a final |
790 |
energy 15~kcal/mol below the original $\lambda = 0$ configuration. |
791 |
When CO is not present and this reaction coordinate is followed, the |
792 |
process is endothermic by 3~kcal/mol. The difference in the relative |
793 |
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present |
794 |
provides strong support for CO-mediated Pt-Pt interactions giving rise |
795 |
to the doubling reconstruction. |
796 |
|
797 |
%lambda progression of Pt -> shoving its way into the step |
798 |
\begin{figure}[H] |
799 |
\includegraphics[width=\linewidth]{EPS_rxnCoord} |
800 |
\caption{Points along a possible reaction coordinate for CO-mediated |
801 |
edge doubling. Here, a CO-bound adatom burrows into an established |
802 |
step edge and displaces an edge atom onto the upper terrace along a |
803 |
curvilinear path. The approximate barrier for the process is |
804 |
20~kcal/mol, and the complete process is exothermic by 15~kcal/mol |
805 |
in the presence of CO, but is endothermic by 3~kcal/mol without CO.} |
806 |
\label{fig:lambda} |
807 |
\end{figure} |
808 |
|
809 |
The mechanism for doubling on the Pt(557) surface appears to require |
810 |
the cooperation of at least two distinct processes. For complete |
811 |
doubling of a layer to occur there must be a breakup of one |
812 |
terrace. These atoms must then ``disappear'' from that terrace, either |
813 |
by travelling to the terraces above or below their original levels. |
814 |
The presence of CO helps explain mechanisms for both of these |
815 |
situations. There must be sufficient breakage of the step-edge to |
816 |
increase the concentration of adatoms on the surface and these adatoms |
817 |
must then undergo the burrowing highlighted above (or a comparable |
818 |
mechanism) to create the double layer. With sufficient time, these |
819 |
mechanisms working in concert lead to the formation of a double layer. |
820 |
|
821 |
\subsection{CO Removal and double layer stability} |
822 |
Once the double layers had formed on the 50\%~Pt system, they remained |
823 |
stable for the rest of the simulation time with minimal movement. |
824 |
Random fluctuations that involved small clusters or divots were |
825 |
observed, but these features typically healed within a few |
826 |
nanoseconds. Within our simulations, the formation of the double |
827 |
layer appeared to be irreversible and a double layer was never |
828 |
observed to split back into two single layer step-edges while CO was |
829 |
present. |
830 |
|
831 |
To further gauge the effect CO has on this surface, additional |
832 |
simulations were run starting from a late configuration of the 50\%~Pt |
833 |
system that had already formed double layers. These simulations then |
834 |
had their CO molecules suddenly removed. The double layer broke apart |
835 |
rapidly in these simulations, showing a well-defined edge-splitting |
836 |
after 100~ps. Configurations of this system are shown in Figure |
837 |
\ref{fig:breaking}. The coloring of the top and bottom layers helps to |
838 |
show how much mixing the edges experience as they split. These systems |
839 |
were only examined for 10~ns, and within that time despite the initial |
840 |
rapid splitting, the edges only moved another few \AA~apart. It is |
841 |
possible that with longer simulation times, the (557) surface recovery |
842 |
observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered. |
843 |
|
844 |
%breaking of the double layer upon removal of CO |
845 |
\begin{figure}[H] |
846 |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} |
847 |
\caption{Behavior of an established (111) double step after removal of |
848 |
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the |
849 |
removal of CO. Nearly immediately after the CO is removed, the |
850 |
step edge reforms in a (100) configuration, which is also the step |
851 |
type seen on clean (557) surfaces. The step separation involves |
852 |
significant mixing of the lower and upper atoms at the edge.} |
853 |
\label{fig:breaking} |
854 |
\end{figure} |
855 |
|
856 |
|
857 |
%Peaks! |
858 |
%\begin{figure}[H] |
859 |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
860 |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
861 |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
862 |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
863 |
%\label{fig:peaks} |
864 |
%\end{figure} |
865 |
|
866 |
|
867 |
%Don't think I need this |
868 |
%clean surface... |
869 |
%\begin{figure}[H] |
870 |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF} |
871 |
%\caption{} |
872 |
|
873 |
%\end{figure} |
874 |
%\label{fig:clean} |
875 |
|
876 |
|
877 |
\section{Conclusion} |
878 |
The strength and directionality of the Pt-CO binding interaction, as |
879 |
well as the large quadrupolar repulsion between atop-bound CO |
880 |
molecules, help to explain the observed increase in surface mobility |
881 |
of Pt(557) and the resultant reconstruction into a double-layer |
882 |
configuration at the highest simulated CO-coverages. The weaker Au-CO |
883 |
interaction results in significantly lower adataom diffusion |
884 |
constants, less step-wandering, and a lack of the double layer |
885 |
reconstruction on the Au(557) surface. |
886 |
|
887 |
An in-depth examination of the energetics shows the important role CO |
888 |
plays in increasing step-breakup and in facilitating edge traversal |
889 |
which are both necessary for double layer formation. |
890 |
|
891 |
%Things I am not ready to remove yet |
892 |
|
893 |
%Table of Diffusion Constants |
894 |
%Add gold?M |
895 |
% \begin{table}[H] |
896 |
% \caption{} |
897 |
% \centering |
898 |
% \begin{tabular}{| c | cc | cc | } |
899 |
% \hline |
900 |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
901 |
% \hline |
902 |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
903 |
% \hline |
904 |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
905 |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
906 |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
907 |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
908 |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
909 |
% \hline |
910 |
% \end{tabular} |
911 |
% \end{table} |
912 |
|
913 |
\begin{acknowledgement} |
914 |
We gratefully acknowledge conversations with Dr. William |
915 |
F. Schneider and Dr. Feng Tao. Support for this project was |
916 |
provided by the National Science Foundation under grant CHE-0848243 |
917 |
and by the Center for Sustainable Energy at Notre Dame |
918 |
(cSEND). Computational time was provided by the Center for Research |
919 |
Computing (CRC) at the University of Notre Dame. |
920 |
\end{acknowledgement} |
921 |
\newpage |
922 |
\bibstyle{achemso} |
923 |
\bibliography{COonPtAu} |
924 |
%\end{doublespace} |
925 |
|
926 |
\begin{tocentry} |
927 |
\begin{wrapfigure}{l}{0.5\textwidth} |
928 |
\begin{center} |
929 |
\includegraphics[width=\linewidth]{TOC_doubleLayer} |
930 |
\end{center} |
931 |
\end{wrapfigure} |
932 |
A reconstructed Pt(557) surface after 86~ns exposure to a half a |
933 |
monolayer of CO. The double layer that forms is a result of |
934 |
CO-mediated step-edge wandering as well as a burrowing mechanism that |
935 |
helps lift edge atoms onto an upper terrace. |
936 |
\end{tocentry} |
937 |
|
938 |
\end{document} |