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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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\bibliographystyle{achemso} |
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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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\begin{document} |
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%% |
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%Introduction |
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% Experimental observations |
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%Summary |
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%% |
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%Title |
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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, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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|
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%Date |
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\date{Dec 15, 2012} |
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%authors |
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|
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% make the title |
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\maketitle |
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\begin{doublespace} |
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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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\newpage |
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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 an effort to understand the mechanism and timescale for |
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surface restructuring using molecular simulations. Since the dynamics |
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of the process is of particular interest, we utilize classical force |
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fields that represent a compromise between chemical accuracy and the |
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computational efficiency necessary to observe the process of interest. |
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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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Since restructuring occurs as a result of specific interactions of the |
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catalyst with adsorbates, two metal systems exposed to carbon monoxide |
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were examined in this work. The Pt(557) surface has already been shown |
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to reconstruct under certain conditions. The Au(557) surface, because |
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of a weaker interaction with CO, is less likely to undergo this kind |
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of reconstruction. MORE HERE ON PT AND AU PREVIOUS WORK. |
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|
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%Platinum molecular dynamics |
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%gold molecular dynamics |
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\section{Simulation Methods} |
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The challenge in modeling any solid/gas interface problem is the |
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development of a sufficiently general yet computationally tractable |
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model of the chemical interactions between the surface atoms and |
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adsorbates. Since the interfaces involved are quite large (10$^3$ - |
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10$^6$ atoms) and respond slowly to perturbations, {\it ab initio} |
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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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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, while modeling the CO using a rigid |
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three-site model developed by Straub and Karplus for studying |
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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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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 al.} is among the |
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fastest of these density functional approaches.\cite{Ercolessi88} In |
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all of these models, atoms are conceptualized as a positively charged |
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core with a radially-decaying valence electron distribution. To |
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calculate the energy for embedding the core at a particular location, |
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the electron density due to the valence electrons at all of the other |
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atomic sites is computed at atom $i$'s location, |
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parameter sets. The glue model of Ercolessi {\it et |
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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}) |
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\end{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 an pairwise term that is meant to represent the |
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overlap of the two positively charged cores. |
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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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% 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 potentials |
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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 |
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simulations of bulk and nanoparticle |
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properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq} |
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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} crack |
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propagation,\cite{BECQUART:1993rg} and alloying |
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dynamics.\cite{Shibata:2002hh} All of these potentials have their |
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strengths and weaknesses. One of the strengths common to all of the |
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methods is the relatively large library of metals for which these |
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potentials have been |
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parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
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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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Since previous explanations for the surface rearrangements center on |
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the large linear quadrupole moment of carbon monoxide, the model |
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chosen for this molecule exhibits this property in an efficient |
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manner. We used a model first proposed by Karplus and Straub to study |
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the photodissociation of CO from myoglobin.\cite{Straub} The Straub and |
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Karplus model is a rigid three site model which places a massless M |
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site at the center of mass along the CO bond. The geometry used along |
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with the interaction parameters are reproduced in Table~1. The effective |
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dipole moment, calculated from the assigned charges, is still |
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small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
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to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
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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 the CO-CO |
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interactions borrowed from Ref. \bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA~, energies are |
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in kcal/mol, and charges are in atomic units.} |
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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 & 0.0262 & 3.83 & -0.75 \\ |
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\textbf{O} & 0.4843 & 0.1591 & 3.12 & -0.85 \\ |
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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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\subsection{Cross-Interactions between the metals and carbon monoxide} |
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|
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Since the adsorption of CO onto a platinum surface has been the focus |
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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. Parameters reported by Korzeniewski {\it et |
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al.}\cite{Pons:1986} were a starting point for our fits, which were |
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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). This resulting binding energies are on the higher |
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side of the experimentally-reported values. 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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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 parameterized to a Morse potential with a large |
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range parameter ($r_o$). In most cases, this contributes a weak |
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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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%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 fit using Lennard-Jones and |
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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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|
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The fits were refined against gas-surface DFT calculations with a |
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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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{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
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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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Ionic relaxations were performed until the energy difference between |
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subsequent steps was less than $10^{-8}$ Ry. In testing the CO-Au |
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interaction, Au(111) supercells were constructed of four layers of 4 |
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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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Supercell calculations were performed nonspin-polarized with a 4 x 4 x |
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4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
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zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
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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 |
282 |
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performed until the energy difference between subsequent steps |
283 |
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was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
284 |
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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 |
286 |
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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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|
290 |
|
%Hint at future work |
291 |
< |
The parameters employed in this work are shown in Table 2 and the |
292 |
< |
binding energies on the 111 surfaces are displayed in Table 3. To |
293 |
< |
speed up the computations, charge transfer and polarization are not |
294 |
< |
being treated in this model, although these effects are likely to |
295 |
< |
affect binding energies and binding site |
278 |
< |
preferences.\cite{Deshlahra:2012} |
291 |
> |
The parameters employed for the metal-CO cross-interactions in this work |
292 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
293 |
> |
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
294 |
> |
and polarization are neglected in this model, although these effects could have |
295 |
> |
an effect on binding energies and binding site preferences. |
296 |
|
|
297 |
|
%Table of Parameters |
298 |
|
%Pt Parameter Set 9 |
299 |
|
%Au Parameter Set 35 |
300 |
|
\begin{table}[H] |
301 |
< |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
302 |
< |
interactions are modeled with Lennard-Jones potential, while the |
303 |
< |
(mostly-repulsive) metal-O interactions were fit to Morse |
301 |
> |
\caption{Parameters for the metal-CO cross-interactions. Metal-C |
302 |
> |
interactions are modeled with Lennard-Jones potentials, while the |
303 |
> |
metal-O interactions were fit to broad Morse |
304 |
|
potentials. Distances are given in \AA~and energies in kcal/mol. } |
305 |
|
\centering |
306 |
|
\begin{tabular}{| c | cc | c | ccc |} |
312 |
|
|
313 |
|
\hline |
314 |
|
\end{tabular} |
315 |
+ |
\label{tab:co_parameters} |
316 |
|
\end{table} |
317 |
|
|
318 |
|
%Table of energies |
319 |
|
\begin{table}[H] |
320 |
< |
\caption{Adsorption energies for CO on M(111) using the potentials |
321 |
< |
described in this work. All values are in eV} |
320 |
> |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
321 |
> |
described in this work. All values are in eV.} |
322 |
|
\centering |
323 |
|
\begin{tabular}{| c | cc |} |
324 |
|
\hline |
327 |
|
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
328 |
|
(Ref. \protect\cite{Kelemen:1979}) \\ |
329 |
|
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
330 |
< |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
330 |
> |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
331 |
|
\hline |
332 |
|
\end{tabular} |
333 |
+ |
\label{tab:co_energies} |
334 |
|
\end{table} |
335 |
|
|
317 |
– |
\subsection{Pt(557) and Au(557) metal interfaces} |
336 |
|
|
337 |
< |
Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a |
338 |
< |
FCC crystal that have been cut along the 557 plane so that they are |
339 |
< |
periodic in the {\it x} and {\it y} directions, and have been rotated |
340 |
< |
to expose two parallel 557 cuts along the positive and negative {\it |
341 |
< |
z}-axis. Simulations of the bare metal interfaces at temperatures |
342 |
< |
ranging from 300~K to 1200~K were done to observe the relative |
337 |
> |
\subsection{Validation of forcefield selections} |
338 |
> |
By calculating minimum energies for commensurate systems of |
339 |
> |
single and double layer Pt and Au systems with 0 and 50\% coverages |
340 |
> |
(arranged in a c(2x4) pattern), our forcefield selections were able to be |
341 |
> |
indirectly compared to results shown in the supporting information of Tao |
342 |
> |
{\it et al.} \cite{Tao:2010}. Five layer thick systems, displaying a 557 facet |
343 |
> |
were constructed, each composed of 480 metal atoms. Double layers systems |
344 |
> |
were constructed from six layer thick systems where an entire layer was |
345 |
> |
removed from both displayed facets to create a double step. By design, the |
346 |
> |
double step system also contains 480 atoms, five layers thick, so energy |
347 |
> |
comparisons between the arrangements can be made directly. The positions |
348 |
> |
of the atoms were allowed to relax, along with the box sizes, before a |
349 |
> |
minimum energy was calculated. Carbon monoxide, equivalent to 50\% |
350 |
> |
coverage on one side of the metal system was added in a c(2x4) arrangement |
351 |
> |
and again allowed to relax before a minimum energy was calculated. |
352 |
> |
|
353 |
> |
Energies for the various systems are displayed in Table ~\ref{tab:steps}. Examining |
354 |
> |
the Pt systems first, it is apparent that the double layer system is slightly less stable |
355 |
> |
then the original single step. However, upon addition of carbon monoxide, the |
356 |
> |
stability is reversed and the double layer system becomes more stable. This result |
357 |
> |
is in agreement with DFT calculations in Tao {\it et al.}\cite{Tao:2010}, who also show |
358 |
> |
that the addition of CO leads to a reversal in the most stable system. While our |
359 |
> |
results agree qualitatively, quantitatively, they are approximately an order of magnitude |
360 |
> |
different. Looking at additional stability per atom in kcal/mol, the DFT calculations suggest |
361 |
> |
an increased stability of 0.1 kcal/mol per Pt atom, whereas we are seeing closer to a 0.4 kcal/mol |
362 |
> |
increase in stability per Pt atom. |
363 |
> |
|
364 |
> |
The gold systems show a much smaller energy difference between the single and double |
365 |
> |
systems, likely arising from their lower energy per atom values. Additionally, the weaker |
366 |
> |
binding of CO to Au is evidenced by the much smaller energy change between the two systems, |
367 |
> |
when compared to the Pt results. This limited change helps explain our lack of any reconstruction |
368 |
> |
on the Au systems. |
369 |
> |
|
370 |
> |
|
371 |
> |
%Table of single step double step calculations |
372 |
> |
\begin{table}[H] |
373 |
> |
\caption{Minimized single point energies of unit cell crystals displaying (S)ingle or (D)double steps. Systems are periodic along and perpendicular to the step-edge axes with a large vacuum above the displayed 557 facet. The addition of CO in a 50\% c(2x4) coverage acts as a stabilizing presence and suggests a driving force for the observed reconstruction on the highest coverage Pt system. All energies are in kcal/mol.} |
374 |
> |
\centering |
375 |
> |
\begin{tabular}{| c | c | c | c | c | c | c |} |
376 |
> |
\hline |
377 |
> |
\textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Unit-Cell Energy} & \textbf{Energy per M} & \textbf{Energy per CO} & \textbf{Difference per M} \\ |
378 |
> |
\hline |
379 |
> |
Pt(557)-S & 480 & 0 & -61142.624 & -127.381 & - & 0 \\ |
380 |
> |
Pt(557)-D & 480 & 0 & -61027.841 & -127.141 & - & 0.240 \\ |
381 |
> |
\hline |
382 |
> |
Pt(557)-S & 480 & 40 & -62960.289 & -131.167 & -45.442 & 0 \\ |
383 |
> |
Pt(557)-D & 480 & 44 & -63040.007 & -131.333 & -45.731 & -0.166\\ |
384 |
> |
\hline |
385 |
> |
\hline |
386 |
> |
Au(557)-S & 480 & 0 & -41879.286 & -87.249 & - &0 \\ |
387 |
> |
Au(557)-D & 480 & 0 & -41799.714 & -87.084 & - & 0.165 \\ |
388 |
> |
\hline |
389 |
> |
Au(557)-S & 480 & 40 & -42423.899 & -88.381 & -13.615 & 0 \\ |
390 |
> |
Au(557)-D & 480 & 44 & -42428.738 & -88.393 & -14.296 & -0.012 \\ |
391 |
> |
\hline |
392 |
> |
\end{tabular} |
393 |
> |
\label{tab:steps} |
394 |
> |
\end{table} |
395 |
> |
|
396 |
> |
|
397 |
> |
\subsection{Pt(557) and Au(557) metal interfaces} |
398 |
> |
Our Pt system is an orthorhombic periodic box of dimensions |
399 |
> |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
400 |
> |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
401 |
> |
are 9 and 8 atoms deep respectively, corresponding to a slab |
402 |
> |
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
403 |
> |
The systems are arranged in a FCC crystal that have been cut |
404 |
> |
along the (557) plane so that they are periodic in the {\it x} and |
405 |
> |
{\it y} directions, and have been oriented to expose two aligned |
406 |
> |
(557) cuts along the extended {\it z}-axis. Simulations of the |
407 |
> |
bare metal interfaces at temperatures ranging from 300~K to |
408 |
> |
1200~K were performed to confirm the relative |
409 |
|
stability of the surfaces without a CO overlayer. |
410 |
|
|
411 |
< |
The different bulk (and surface) melting temperatures (1337~K for Au |
412 |
< |
and 2045~K for Pt) suggest that the reconstruction may happen at |
413 |
< |
different temperatures for the two metals. To copy experimental |
414 |
< |
conditions for the CO-exposed surfaces, the bare surfaces were |
415 |
< |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
416 |
< |
respectively for 100 ps. Each surface was exposed to a range of CO |
417 |
< |
that was initially placed in the vacuum region. Upon full adsorption, |
418 |
< |
these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
419 |
< |
coverage. Because of the difference in binding energies, the platinum |
420 |
< |
systems very rarely had CO that was not bound to the surface, while |
421 |
< |
the gold surfaces often had a significant CO population in the gas |
422 |
< |
phase. These systems were allowed to reach thermal equilibrium (over |
423 |
< |
5 ns) before being shifted to the microcanonical (NVE) ensemble for |
424 |
< |
data collection. All of the systems examined had at least 40 ns in the |
425 |
< |
data collection stage, although simulation times for some of the |
426 |
< |
systems exceeded 200ns. All simulations were run using the open |
427 |
< |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD} |
411 |
> |
The different bulk melting temperatures predicted by EAM |
412 |
> |
(1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for |
413 |
> |
Pt\cite{Pt:melting}) suggest that any reconstructions should happen at |
414 |
> |
different temperatures for the two metals. The bare Au and Pt |
415 |
> |
surfaces were initially run in the canonical (NVT) ensemble at 800~K |
416 |
> |
and 1000~K respectively for 100 ps. The two surfaces were relatively |
417 |
> |
stable at these temperatures when no CO was present, but experienced |
418 |
> |
increased surface mobility on addition of CO. Each surface was then |
419 |
> |
dosed with different concentrations of CO that was initially placed in |
420 |
> |
the vacuum region. Upon full adsorption, these concentrations |
421 |
> |
correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher |
422 |
> |
coverages resulted in the formation of a double layer of CO, which |
423 |
> |
introduces artifacts that are not relevant to (557) reconstruction. |
424 |
> |
Because of the difference in binding energies, nearly all of the CO |
425 |
> |
was bound to the Pt surface, while the Au surfaces often had a |
426 |
> |
significant CO population in the gas phase. These systems were |
427 |
> |
allowed to reach thermal equilibrium (over 5~ns) before being run in |
428 |
> |
the microcanonical (NVE) ensemble for data collection. All of the |
429 |
> |
systems examined had at least 40~ns in the data collection stage, |
430 |
> |
although simulation times for some Pt of the systems exceeded 200~ns. |
431 |
> |
Simulations were carried out using the open source molecular dynamics |
432 |
> |
package, OpenMD.\cite{Ewald,OOPSE,openmd} |
433 |
|
|
434 |
< |
% Just results, leave discussion for discussion section |
435 |
< |
% structure |
436 |
< |
% Pt: step wandering, double layers, no triangular motifs |
348 |
< |
% Au: step wandering, no double layers |
349 |
< |
% dynamics |
350 |
< |
% diffusion |
351 |
< |
% time scale, formation, breakage |
434 |
> |
|
435 |
> |
% RESULTS |
436 |
> |
% |
437 |
|
\section{Results} |
438 |
|
\subsection{Structural remodeling} |
439 |
< |
Tao {\it et al.} showed experimentally that the Pt(557) surface undergoes |
440 |
< |
two separate reconstructions upon CO adsorption.\cite{Tao:2010} The first |
441 |
< |
reconstruction involves a doubling of the step height and plateau length. Similar |
442 |
< |
behavior has been seen to occur on numerous surfaces at varying conditions.\cite{Williams:1994,Williams:1991,Pearl} |
443 |
< |
Of the two systems we examined, the Platinum system showed the most surface |
444 |
< |
reconstruction. Additionally, the amount of reconstruction appears to be |
445 |
< |
dependent on the amount of CO adsorbed upon the surface. This result is likely |
446 |
< |
related to the effect that coverage has on surface diffusion. While both systems |
447 |
< |
displayed step edge wandering, only the Pt surface underwent doubling within |
448 |
< |
the time scales we were modeling. Specifically only the 50 \% coverage Pt system |
449 |
< |
was observed to undergo a complete doubling in the time scales we were able to monitor. |
365 |
< |
This event encouraged us to allow that specific system to run continuously during which two |
366 |
< |
more double layers were created. The other systems, not displaying any large scale changes |
367 |
< |
of interest, were all stopped after 40 ns of simulation. Neverthless, the other Platinum systems tended to show |
368 |
< |
more cumulative lateral movement of the step edges when compared to the Gold systems. |
369 |
< |
The 50 \% Pt system is highlighted in figure \ref{fig:reconstruct} at various times along the |
370 |
< |
simulation showing the evolution of the system. |
439 |
> |
The bare metal surfaces experienced minor roughening of the step-edge |
440 |
> |
because of the elevated temperatures, but the (557) face was stable |
441 |
> |
throughout the simulations. The surfaces of both systems, upon dosage |
442 |
> |
of CO, began to undergo extensive remodeling that was not observed in |
443 |
> |
the bare systems. Reconstructions of the Au systems were limited to |
444 |
> |
breakup of the step-edges and some step wandering. The lower coverage |
445 |
> |
Pt systems experienced similar step edge wandering but to a greater |
446 |
> |
extent. The 50\% coverage Pt system was unique among our simulations |
447 |
> |
in that it formed well-defined and stable double layers through step |
448 |
> |
coalescence, similar to results reported by Tao {\it et |
449 |
> |
al}.\cite{Tao:2010} |
450 |
|
|
451 |
< |
The second reconstruction on the Pt(557) surface observed by Tao involved the |
452 |
< |
formation of triangular clusters that stretched across the plateau between two step edges. |
453 |
< |
Neither system, within our simulated time scales, experiences this reconstruction. A constructed |
454 |
< |
system in which the triangular motifs were constructed on the surface will be explored in future |
455 |
< |
work and is shown in the supporting information. |
451 |
> |
\subsubsection{Step wandering} |
452 |
> |
The bare surfaces for both metals showed minimal step-wandering at |
453 |
> |
their respective temperatures. As the CO coverage increased however, |
454 |
> |
the mobility of the surface atoms, described through adatom diffusion |
455 |
> |
and step-edge wandering, also increased. Except for the 50\% Pt |
456 |
> |
system where step coalescence occurred, the step-edges in the other |
457 |
> |
simulations preferred to keep nearly the same distance between steps |
458 |
> |
as in the original (557) lattice, $\sim$13\AA~for Pt and |
459 |
> |
$\sim$14\AA~for Au. Previous work by Williams {\it et |
460 |
> |
al}.\cite{Williams:1991, Williams:1994} highlights the repulsion |
461 |
> |
that exists between step-edges even when no direct interactions are |
462 |
> |
present in the system. This repulsion is caused by an entropic barrier |
463 |
> |
that arises from the fact that steps cannot cross over one |
464 |
> |
another. This entropic repulsion does not completely define the |
465 |
> |
interactions between steps, however, so it is possible to observe step |
466 |
> |
coalescence on some surfaces.\cite{Williams:1991} The presence and |
467 |
> |
concentration of adsorbates, as shown in this work, can affect |
468 |
> |
step-step interactions, potentially leading to a new surface structure |
469 |
> |
as the thermodynamic equilibrium. |
470 |
|
|
471 |
< |
\subsection{Dynamics} |
472 |
< |
While atomistic-like simulations of stepped surfaces have been performed before \cite{}, they tend to be |
473 |
< |
performed using Monte Carlo techniques\cite{Williams:1991,Williams:1994}. This allows them to efficiently sample the thermodynamic |
474 |
< |
landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM \cite{Pearl}, |
475 |
< |
has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition, ~ 70 s/image |
476 |
< |
provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments |
477 |
< |
of step edges are adept at analyzing such systems, it is important to remember that the edges are made |
478 |
< |
up of individual atoms and thus can be examined in numerous ways. |
479 |
< |
|
480 |
< |
\subsubsection{Transport of surface metal atoms} |
481 |
< |
%forcedSystems/stepSeparation |
482 |
< |
The movement of a step edge is a cooperative effect arising from the individual movements of the atoms |
483 |
< |
making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to |
484 |
< |
experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface. |
485 |
< |
For our surfaces however, the presence of step edges provide a source for mobile metal atoms. Breaking away |
486 |
< |
from the step edge still imposes an energetic penalty around 40 kcal/mole, but is much less than lifting the same metal |
487 |
< |
atom out from the surface, > 60 kcal/mole, and the penalty lowers even further when CO is present in sufficient quantities |
488 |
< |
on the surface, ~20 kcal/mole. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole) |
489 |
< |
and is well able to explore its terrace. Atoms traversing terraces is more difficult, but can be overcome through a joining and lifting stage. |
490 |
< |
By tracking the mobility of individual metal atoms on the Platinum and Gold surfaces we were able to determine |
491 |
< |
the relative diffusion rates and how varying coverages of CO affected the rates. Close |
399 |
< |
observation of the mobile metal atoms showed that they were typically in equilibrium with the |
400 |
< |
step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and |
401 |
< |
two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying |
402 |
< |
the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
403 |
< |
|
404 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations |
405 |
< |
of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but |
406 |
< |
the 2~\AA~ cutoff was to prevent the in-place vibrational movement of atoms from being included in the analysis. |
407 |
< |
Since diffusion on a surface is strongly affected by local structures, in this case the presence of single and double |
408 |
< |
layer step edges, the diffusion parallel to the step edges was determined separately from the diffusion perpendicular |
409 |
< |
to these edges. The parallel and perpendicular diffusion constants are shown in figure \ref{fig:diff}. |
471 |
> |
\subsubsection{Double layers} |
472 |
> |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the |
473 |
> |
Pt(557) surface undergoes two separate reconstructions upon CO |
474 |
> |
adsorption. The first involves a doubling of the step height and |
475 |
> |
plateau length. Similar behavior has been seen on a number of |
476 |
> |
surfaces at varying conditions, including Ni(977) and |
477 |
> |
Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we |
478 |
> |
examined, the Pt system showed a greater propensity for reconstruction |
479 |
> |
because of the larger surface mobility and the greater extent of step |
480 |
> |
wandering. The amount of reconstruction was strongly correlated to |
481 |
> |
the amount of CO adsorbed upon the surface. This appears to be |
482 |
> |
related to the effect that adsorbate coverage has on edge breakup and |
483 |
> |
on the surface diffusion of metal adatoms. Only the 50\% Pt surface |
484 |
> |
underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within |
485 |
> |
the time scales studied here. Over a longer time scale (150~ns) two |
486 |
> |
more double layers formed on this surface. Although double layer |
487 |
> |
formation did not occur in the other Pt systems, they exhibited more |
488 |
> |
step-wandering and roughening compared to their Au counterparts. The |
489 |
> |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
490 |
> |
various times along the simulation showing the evolution of a double |
491 |
> |
layer step-edge. |
492 |
|
|
493 |
< |
\subsubsection{Double layer formation} |
494 |
< |
The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the |
495 |
< |
formation of double layers, seeing as how that was the only system within our observed simulation time |
496 |
< |
that showed the formation. Despite this being the only system where this reconstruction occurs, three separate layers |
497 |
< |
were formed over the extended run time of this system. As mentioned earlier, previous experimental work has given some insight into |
416 |
< |
the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{Williams:1991,Pearl}. |
417 |
< |
As seen in figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into |
418 |
< |
the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, a smooth complete |
419 |
< |
layer has formed. The double layer is complete by 37 ns but is a bit rough. |
420 |
< |
From the appearance of the first node to the initial doubling of the layers ignoring their roughness took ~20 ns. |
421 |
< |
Another ~40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form |
422 |
< |
over a period of 22 ns and 42 ns respectively. |
493 |
> |
The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010} |
494 |
> |
involved the formation of triangular clusters that stretched across |
495 |
> |
the plateau between two step-edges. Neither of the simulated metal |
496 |
> |
interfaces, within the 40~ns time scale or the extended time of 150~ns |
497 |
> |
for the 50\% Pt system, experienced this reconstruction. |
498 |
|
|
499 |
|
%Evolution of surface |
500 |
|
\begin{figure}[H] |
501 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
502 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
503 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
504 |
< |
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
505 |
< |
doubling of the layers appears only after two adjacent step edges |
501 |
> |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} |
502 |
> |
\caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a) |
503 |
> |
258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after |
504 |
> |
exposure. Disruption of the (557) step-edges occurs quickly. The |
505 |
> |
doubling of the layers appears only after two adjacent step-edges |
506 |
|
touch. The circled spot in (b) nucleated the growth of the double |
507 |
|
step observed in the later configurations.} |
508 |
|
\label{fig:reconstruct} |
509 |
|
\end{figure} |
510 |
|
|
511 |
+ |
\subsection{Dynamics} |
512 |
+ |
Previous experimental work by Pearl and Sibener\cite{Pearl}, using |
513 |
+ |
STM, has been able to capture the coalescence of steps on Ni(977). The |
514 |
+ |
time scale of the image acquisition, $\sim$70~s/image, provides an |
515 |
+ |
upper bound for the time required for the doubling to occur. By |
516 |
+ |
utilizing Molecular Dynamics we are able to probe the dynamics of |
517 |
+ |
these reconstructions at elevated temperatures and in this section we |
518 |
+ |
provide data on the timescales for transport properties, |
519 |
+ |
e.g. diffusion and layer formation time. |
520 |
+ |
|
521 |
+ |
|
522 |
+ |
\subsubsection{Transport of surface metal atoms} |
523 |
+ |
%forcedSystems/stepSeparation |
524 |
+ |
|
525 |
+ |
The wandering of a step-edge is a cooperative effect arising from the |
526 |
+ |
individual movements of the atoms making up the steps. An ideal metal |
527 |
+ |
surface displaying a low index facet, (111) or (100), is unlikely to |
528 |
+ |
experience much surface diffusion because of the large energetic |
529 |
+ |
barrier that must be overcome to lift an atom out of the surface. The |
530 |
+ |
presence of step-edges and other surface features on higher-index |
531 |
+ |
facets provides a lower energy source for mobile metal atoms. Using |
532 |
+ |
our potential model, single-atom break-away from a step-edge on a |
533 |
+ |
clean surface still imposes an energetic penalty around |
534 |
+ |
$\sim$~45~kcal/mol, but this is certainly easier than lifting the same |
535 |
+ |
metal atom vertically out of the surface, \textgreater~60~kcal/mol. |
536 |
+ |
The penalty lowers significantly when CO is present in sufficient |
537 |
+ |
quantities on the surface. For certain distributions of CO, the |
538 |
+ |
energetic penalty can fall to as low as $\sim$~20~kcal/mol. The |
539 |
+ |
configurations that create these lower barriers are detailed in the |
540 |
+ |
discussion section below. |
541 |
+ |
|
542 |
+ |
Once an adatom exists on the surface, the barrier for diffusion is |
543 |
+ |
negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are |
544 |
+ |
then able to explore the terrace before rejoining either their |
545 |
+ |
original step-edge or becoming a part of a different edge. It is an |
546 |
+ |
energetically unfavorable process with a high barrier for an atom to |
547 |
+ |
traverse to a separate terrace although the presence of CO can lower |
548 |
+ |
the energy barrier required to lift or lower an adatom. By tracking |
549 |
+ |
the mobility of individual metal atoms on the Pt and Au surfaces we |
550 |
+ |
were able to determine the relative diffusion constants, as well as |
551 |
+ |
how varying coverages of CO affect the diffusion. Close observation of |
552 |
+ |
the mobile metal atoms showed that they were typically in equilibrium |
553 |
+ |
with the step-edges. At times, their motion was concerted, and two or |
554 |
+ |
more adatoms would be observed moving together across the surfaces. |
555 |
+ |
|
556 |
+ |
A particle was considered ``mobile'' once it had traveled more than |
557 |
+ |
2~\AA~ between saved configurations of the system (typically 10-100 |
558 |
+ |
ps). A mobile atom would typically travel much greater distances than |
559 |
+ |
this, but the 2~\AA~cutoff was used to prevent swamping the diffusion |
560 |
+ |
data with the in-place vibrational movement of buried atoms. Diffusion |
561 |
+ |
on a surface is strongly affected by local structures and the presence |
562 |
+ |
of single and double layer step-edges causes the diffusion parallel to |
563 |
+ |
the step-edges to be larger than the diffusion perpendicular to these |
564 |
+ |
edges. Parallel and perpendicular diffusion constants are shown in |
565 |
+ |
Figure \ref{fig:diff}. Diffusion parallel to the step-edge is higher |
566 |
+ |
than diffusion perpendicular to the edge because of the lower energy |
567 |
+ |
barrier associated with sliding along an edge compared to breaking |
568 |
+ |
away to form an isolated adatom. |
569 |
+ |
|
570 |
+ |
%Diffusion graph |
571 |
|
\begin{figure}[H] |
572 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
572 |
> |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1} |
573 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
574 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
575 |
< |
($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO |
576 |
< |
surface coverage. Diffusion parallel to the step edge is higher |
577 |
< |
than that perpendicular to the edge because of the lower energy |
578 |
< |
barrier associated with going from approximately 7 nearest neighbors |
579 |
< |
to 5, as compared to the 3 of an adatom. Additionally, the observed |
445 |
< |
maximum and subsequent decrease for the Pt system suggests that the |
446 |
< |
CO self-interactions are playing a significant role with regards to |
447 |
< |
movement of the platinum atoms around and more importantly across |
448 |
< |
the surface. } |
575 |
> |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
576 |
> |
surface coverage. The two reported diffusion constants for the 50\% |
577 |
> |
Pt system correspond to a 20~ns period before the formation of the |
578 |
> |
double layer (upper points), and to the full 40~ns sampling period |
579 |
> |
(lower points).} |
580 |
|
\label{fig:diff} |
581 |
|
\end{figure} |
582 |
|
|
583 |
+ |
The weaker Au-CO interaction is evident in the weak CO-coverage |
584 |
+ |
dependance of Au diffusion. This weak interaction leads to lower |
585 |
+ |
observed coverages when compared to dosage amounts. This further |
586 |
+ |
limits the effect the CO can have on surface diffusion. The correlation |
587 |
+ |
between coverage and Pt diffusion rates shows a near linear relationship |
588 |
+ |
at the earliest times in the simulations. Following double layer formation, |
589 |
+ |
however, there is a precipitous drop in adatom diffusion. As the double |
590 |
+ |
layer forms, many atoms that had been tracked for mobility data have |
591 |
+ |
now been buried, resulting in a smaller reported diffusion constant. A |
592 |
+ |
secondary effect of higher coverages is CO-CO cross interactions that |
593 |
+ |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
594 |
+ |
This effect would become evident only at higher coverages. A detailed |
595 |
+ |
account of Pt adatom energetics follows in the Discussion. |
596 |
+ |
|
597 |
+ |
\subsubsection{Dynamics of double layer formation} |
598 |
+ |
The increased diffusion on Pt at the higher CO coverages is the primary |
599 |
+ |
contributor to double layer formation. However, this is not a complete |
600 |
+ |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
601 |
+ |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
602 |
+ |
system, one double layer formed within the first 40~ns of simulation time, |
603 |
+ |
while two more were formed as the system was allowed to run for an |
604 |
+ |
additional 110~ns (150~ns total). This suggests that this reconstruction |
605 |
+ |
is a rapid process and that the previously mentioned upper bound is a |
606 |
+ |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
607 |
+ |
appearance of a double layer appears at 19~ns into the simulation. |
608 |
+ |
Within 12~ns of this nucleation event, nearly half of the step has formed |
609 |
+ |
the double layer and by 86~ns the complete layer has flattened out. |
610 |
+ |
From the appearance of the first nucleation event to the first observed |
611 |
+ |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
612 |
+ |
necessary for the layer to completely straighten. The other two layers in |
613 |
+ |
this simulation formed over periods of 22~ns and 42~ns respectively. |
614 |
+ |
A possible explanation for this rapid reconstruction is the elevated |
615 |
+ |
temperatures under which our systems were simulated. The process |
616 |
+ |
would almost certainly take longer at lower temperatures. Additionally, |
617 |
+ |
our measured times for completion of the doubling after the appearance |
618 |
+ |
of a nucleation site are likely affected by our periodic boxes. A longer |
619 |
+ |
step-edge will likely take longer to ``zipper''. |
620 |
|
|
621 |
|
|
454 |
– |
|
622 |
|
%Discussion |
623 |
|
\section{Discussion} |
624 |
< |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
625 |
< |
Pt (557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
626 |
< |
were able to capture the dynamic processes inherent within this reconstruction. |
624 |
> |
We have shown that a classical potential is able to model the initial |
625 |
> |
reconstruction of the Pt(557) surface upon CO adsorption, and have |
626 |
> |
reproduced the double layer structure observed by Tao {\it et |
627 |
> |
al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be |
628 |
> |
rapid -- occurring within 100 ns of the initial exposure to CO. Here |
629 |
> |
we discuss the features of the classical potential that are |
630 |
> |
contributing to the stability and speed of the Pt(557) reconstruction. |
631 |
|
|
632 |
< |
\subsection{Mechanism for restructuring} |
633 |
< |
The increased computational cost to examine this system using molecular dynamics rather than |
634 |
< |
a Monte Carlo based approach was necessary so that our predictions on possible mechanisms |
635 |
< |
and driving forces would have support not only from thermodynamic arguments but also from the |
636 |
< |
actual dynamics of the system. |
632 |
> |
\subsection{Diffusion} |
633 |
> |
The perpendicular diffusion constant appears to be the most important |
634 |
> |
indicator of double layer formation. As highlighted in Figure |
635 |
> |
\ref{fig:reconstruct}, the formation of the double layer did not begin |
636 |
> |
until a nucleation site appeared. Williams {\it et |
637 |
> |
al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge |
638 |
> |
repulsion arising from the inability of edge crossing. This repulsion |
639 |
> |
must be overcome to allow step coalescence. A larger |
640 |
> |
$\textbf{D}_\perp$ value implies more step-wandering and a larger |
641 |
> |
chance for the stochastic meeting of two edges to create a nucleation |
642 |
> |
point. Diffusion parallel to the step-edge can help ``zipper'' up a |
643 |
> |
nascent double layer. This helps explain the rapid time scale for |
644 |
> |
double layer completion after the appearance of a nucleation site, while |
645 |
> |
the initial appearance of the nucleation site was unpredictable. |
646 |
|
|
647 |
< |
Comparing the results from simulation to those reported previously by |
648 |
< |
Tao et al. the similarities in the platinum and CO system are quite |
649 |
< |
strong. As shown in figure \ref{fig:reconstruct}, the simulated platinum system under a CO |
650 |
< |
atmosphere will restructure slightly by doubling the terrace |
651 |
< |
heights. The restructuring appears to occur slowly, one to two |
652 |
< |
platinum atoms at a time. Looking at individual snapshots, these |
473 |
< |
adatoms tend to either rise on top of the plateau or break away from |
474 |
< |
the step edge and then diffuse perpendicularly to the step direction |
475 |
< |
until reaching another step edge. This combination of growth and decay |
476 |
< |
of the step edges appears to be in somewhat of a state of dynamic |
477 |
< |
equilibrium. However, once two previously separated edges meet as |
478 |
< |
shown in figure 1.B, this point tends to act as a focus or growth |
479 |
< |
point for the rest of the edge to meet up, akin to that of a |
480 |
< |
zipper. From the handful of cases where a double layer was formed |
481 |
< |
during the simulation, measuring from the initial appearance of a |
482 |
< |
growth point, the double layer tends to be fully formed within |
483 |
< |
$\sim$~35 ns. |
484 |
< |
|
485 |
< |
There are a number of possible mechanisms to explain the role of |
486 |
< |
adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion |
487 |
< |
between adjacent CO molecules adsorbed on the surface is one |
647 |
> |
\subsection{Mechanism for restructuring} |
648 |
> |
Since the Au surface showed no large scale restructuring in any of our |
649 |
> |
simulations, our discussion will focus on the 50\% Pt-CO system which |
650 |
> |
did exhibit doubling. A number of possible mechanisms exist to explain |
651 |
> |
the role of adsorbed CO in restructuring the Pt surface. Quadrupolar |
652 |
> |
repulsion between adjacent CO molecules adsorbed on the surface is one |
653 |
|
possibility. However, the quadrupole-quadrupole interaction is |
654 |
|
short-ranged and is attractive for some orientations. If the CO |
655 |
< |
molecules are ``locked'' in a specific orientation relative to each other however, |
656 |
< |
this explanation gains some weight. The energetic repulsion between two CO |
657 |
< |
located a distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in a |
658 |
< |
vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second nearest-neighbor |
659 |
< |
distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to nearly 0 kcal/mole. SHOW A NUMBER FOR ROTATION. |
660 |
< |
As mentioned above, the energy barrier for surface diffusion of a platinum adatom is only 4 kcal/mole. So this |
661 |
< |
repulsion between CO can help increase the surface diffusion. However, the residence time of CO was examined |
662 |
< |
and while the majority of the CO is on or near the surface throughout the run, it is extremely mobile. This mobility |
663 |
< |
suggests that the CO are more likely to shift their positions without necessarily dragging the platinum along |
664 |
< |
with them. |
655 |
> |
molecules are ``locked'' in a vertical orientation, through atop |
656 |
> |
adsorption for example, this explanation would gain credence. Within |
657 |
> |
the framework of our classical potential, the calculated energetic |
658 |
> |
repulsion between two CO molecules located a distance of |
659 |
> |
2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a |
660 |
> |
vertical orientation, is 8.62 kcal/mol. Moving the CO to the second |
661 |
> |
nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly |
662 |
> |
0. Allowing the CO to rotate away from a purely vertical orientation |
663 |
> |
also lowers the repulsion. When the carbons are locked at a distance |
664 |
> |
of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle |
665 |
> |
between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
666 |
> |
barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
667 |
> |
repulsion between adjacent CO molecules bound to Pt could indeed |
668 |
> |
increase the surface diffusion. However, the residence time of CO on |
669 |
> |
Pt suggests that the CO molecules are extremely mobile, with diffusion |
670 |
> |
constants 40 to 2500 times larger than surface Pt atoms. This mobility |
671 |
> |
suggests that the CO molecules jump between different Pt atoms |
672 |
> |
throughout the simulation. However, they do stay bound to individual |
673 |
> |
Pt atoms for long enough to modify the local energy landscape for the |
674 |
> |
mobile adatoms. |
675 |
|
|
676 |
< |
Another possible and more likely mechanism for the restructuring is in the |
677 |
< |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
678 |
< |
Pt atoms. This could have the effect of increasing surface mobility |
679 |
< |
of these atoms. To test this hypothesis, numerous configurations of |
680 |
< |
CO in varying quantities were arranged on the higher and lower plateaus |
681 |
< |
around a step on a otherwise clean Pt (557) surface. One representative |
682 |
< |
configuration is displayed in figure \ref{fig:lambda}. Single or concerted movement |
683 |
< |
of platinum atoms was then examined to determine possible barriers. Because |
684 |
< |
of the forced movement along a pre-defined reaction coordinate that may differ |
685 |
< |
from the true minimum of this path, only the beginning and ending energies |
686 |
< |
are displayed in table \ref{tab:energies}. The presence of CO at suitable |
687 |
< |
sites can lead to lowered barriers for platinum breaking apart from the step edge. |
688 |
< |
Additionally, as highlighted in figure \ref{fig:lambda}, the presence of CO makes the |
689 |
< |
burrowing and lifting nature favorable, whereas without CO, the process is neutral |
690 |
< |
in terms of energetics. |
676 |
> |
A different interpretation of the above mechanism which takes the |
677 |
> |
large mobility of the CO into account, would be in the destabilization |
678 |
> |
of Pt-Pt interactions due to bound CO. Destabilizing Pt-Pt bonds at |
679 |
> |
the edges could lead to increased step-edge breakup and diffusion. On |
680 |
> |
the bare Pt(557) surface the barrier to completely detach an edge atom |
681 |
> |
is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
682 |
> |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain |
683 |
> |
configurations, cases (e), (g), and (h), the barrier can be lowered to |
684 |
> |
$\sim$23~kcal/mol by the presence of bound CO molecules. In these |
685 |
> |
instances, it becomes energetically favorable to roughen the edge by |
686 |
> |
introducing a small separation of 0.5 to 1.0~\AA. This roughening |
687 |
> |
becomes immediately obvious in simulations with significant CO |
688 |
> |
populations. The roughening is present to a lesser extent on surfaces |
689 |
> |
with lower CO coverage (and even on the bare surfaces), although in |
690 |
> |
these cases it is likely due to random fluctuations that squeeze out |
691 |
> |
step-edge atoms. Step-edge breakup by direct single-atom translations |
692 |
> |
(as suggested by these energy curves) is probably a worst-case |
693 |
> |
scenario. Multistep mechanisms in which an adatom moves laterally on |
694 |
> |
the surface after being ejected would be more energetically favorable. |
695 |
> |
This would leave the adatom alongside the ledge, providing it with |
696 |
> |
five nearest neighbors. While fewer than the seven neighbors it had |
697 |
> |
as part of the step-edge, it keeps more Pt neighbors than the three |
698 |
> |
neighbors an isolated adatom has on the terrace. In this proposed |
699 |
> |
mechanism, the CO quadrupolar repulsion still plays a role in the |
700 |
> |
initial roughening of the step-edge, but not in any long-term bonds |
701 |
> |
with individual Pt atoms. Higher CO coverages create more |
702 |
> |
opportunities for the crowded CO configurations shown in Figure |
703 |
> |
\ref{fig:SketchGraphic}, and this is likely to cause an increased |
704 |
> |
propensity for step-edge breakup. |
705 |
|
|
706 |
+ |
%Sketch graphic of different configurations |
707 |
+ |
\begin{figure}[H] |
708 |
+ |
\includegraphics[width=\linewidth]{COpaths} |
709 |
+ |
\caption{Configurations used to investigate the mechanism of step-edge |
710 |
+ |
breakup on Pt(557). In each case, the central (starred) atom was |
711 |
+ |
pulled directly across the surface away from the step edge. The Pt |
712 |
+ |
atoms on the upper terrace are colored dark grey, while those on the |
713 |
+ |
lower terrace are in white. In each of these configurations, some |
714 |
+ |
of the atoms (highlighted in blue) had CO molecules bound in the |
715 |
+ |
vertical atop position. The energies of these configurations as a |
716 |
+ |
function of central atom displacement are displayed in Figure |
717 |
+ |
\ref{fig:SketchEnergies}.} |
718 |
+ |
\label{fig:SketchGraphic} |
719 |
+ |
\end{figure} |
720 |
+ |
|
721 |
+ |
%energy graph corresponding to sketch graphic |
722 |
+ |
\begin{figure}[H] |
723 |
+ |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison} |
724 |
+ |
\caption{Energies for displacing a single edge atom perpendicular to |
725 |
+ |
the step edge as a function of atomic displacement. Each of the |
726 |
+ |
energy curves corresponds to one of the labeled configurations in |
727 |
+ |
Figure \ref{fig:SketchGraphic}, and the energies are referenced to |
728 |
+ |
the unperturbed step-edge. Certain arrangements of bound CO |
729 |
+ |
(notably configurations g and h) can lower the energetic barrier for |
730 |
+ |
creating an adatom relative to the bare surface (configuration a).} |
731 |
+ |
\label{fig:SketchEnergies} |
732 |
+ |
\end{figure} |
733 |
+ |
|
734 |
+ |
While configurations of CO on the surface are able to increase |
735 |
+ |
diffusion and the likelihood of edge wandering, this does not provide |
736 |
+ |
a complete explanation for the formation of double layers. If adatoms |
737 |
+ |
were constrained to their original terraces then doubling could not |
738 |
+ |
occur. A mechanism for vertical displacement of adatoms at the |
739 |
+ |
step-edge is required to explain the doubling. |
740 |
+ |
|
741 |
+ |
We have discovered one possible mechanism for a CO-mediated vertical |
742 |
+ |
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} |
743 |
+ |
shows four points along a reaction coordinate in which a CO-bound |
744 |
+ |
adatom along the step-edge ``burrows'' into the edge and displaces the |
745 |
+ |
original edge atom onto the higher terrace. A number of events |
746 |
+ |
similar to this mechanism were observed during the simulations. We |
747 |
+ |
predict an energetic barrier of 20~kcal/mol for this process (in which |
748 |
+ |
the displaced edge atom follows a curvilinear path into an adjacent |
749 |
+ |
3-fold hollow site). The barrier heights we obtain for this reaction |
750 |
+ |
coordinate are approximate because the exact path is unknown, but the |
751 |
+ |
calculated energy barriers would be easily accessible at operating |
752 |
+ |
conditions. Additionally, this mechanism is exothermic, with a final |
753 |
+ |
energy 15~kcal/mol below the original $\lambda = 0$ configuration. |
754 |
+ |
When CO is not present and this reaction coordinate is followed, the |
755 |
+ |
process is endothermic by 3~kcal/mol. The difference in the relative |
756 |
+ |
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present |
757 |
+ |
provides strong support for CO-mediated Pt-Pt interactions giving rise |
758 |
+ |
to the doubling reconstruction. |
759 |
+ |
|
760 |
|
%lambda progression of Pt -> shoving its way into the step |
761 |
|
\begin{figure}[H] |
762 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
763 |
< |
\caption{A model system of the Pt 557 surface was used as the framework for a reaction coordinate. |
764 |
< |
Various numbers, placements, and rotations of CO were examined. The one displayed was a |
765 |
< |
representative sample. As shown in Table , relative to the energy at 0\% there is a slight decrease |
766 |
< |
upon insertion of the platinum atom into the step edge along with the resultant lifting of the other |
767 |
< |
platinum atom.} |
762 |
> |
\includegraphics[width=\linewidth]{EPS_rxnCoord} |
763 |
> |
\caption{Points along a possible reaction coordinate for CO-mediated |
764 |
> |
edge doubling. Here, a CO-bound adatom burrows into an established |
765 |
> |
step edge and displaces an edge atom onto the upper terrace along a |
766 |
> |
curvilinear path. The approximate barrier for the process is |
767 |
> |
20~kcal/mol, and the complete process is exothermic by 15~kcal/mol |
768 |
> |
in the presence of CO, but is endothermic by 3~kcal/mol without CO.} |
769 |
|
\label{fig:lambda} |
770 |
|
\end{figure} |
771 |
|
|
772 |
+ |
The mechanism for doubling on the Pt(557) surface appears to require |
773 |
+ |
the cooperation of at least two distinct processes. For complete |
774 |
+ |
doubling of a layer to occur there must be a breakup of one |
775 |
+ |
terrace. These atoms must then ``disappear'' from that terrace, either |
776 |
+ |
by travelling to the terraces above or below their original levels. |
777 |
+ |
The presence of CO helps explain mechanisms for both of these |
778 |
+ |
situations. There must be sufficient breakage of the step-edge to |
779 |
+ |
increase the concentration of adatoms on the surface and these adatoms |
780 |
+ |
must then undergo the burrowing highlighted above (or a comparable |
781 |
+ |
mechanism) to create the double layer. With sufficient time, these |
782 |
+ |
mechanisms working in concert lead to the formation of a double layer. |
783 |
|
|
784 |
+ |
\subsection{CO Removal and double layer stability} |
785 |
+ |
Once the double layers had formed on the 50\%~Pt system, they remained |
786 |
+ |
stable for the rest of the simulation time with minimal movement. |
787 |
+ |
Random fluctuations that involved small clusters or divots were |
788 |
+ |
observed, but these features typically healed within a few |
789 |
+ |
nanoseconds. Within our simulations, the formation of the double |
790 |
+ |
layer appeared to be irreversible and a double layer was never |
791 |
+ |
observed to split back into two single layer step-edges while CO was |
792 |
+ |
present. |
793 |
|
|
794 |
< |
\subsection{Diffusion} |
795 |
< |
As shown in the results section, the diffusion parallel to the step edge tends to be |
796 |
< |
much faster than that perpendicular to the step edge. Additionally, the coverage |
797 |
< |
of CO appears to play a slight role in relative rates of diffusion, as shown in figure \ref{fig:diff} |
798 |
< |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
799 |
< |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
800 |
< |
appears, parallel diffusion, along the now slightly angled step edge, will allow for |
801 |
< |
a faster formation of the double layer than if the entire process were dependent on |
802 |
< |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
803 |
< |
more likely a growth point is to be formed. |
804 |
< |
\\ |
794 |
> |
To further gauge the effect CO has on this surface, additional |
795 |
> |
simulations were run starting from a late configuration of the 50\%~Pt |
796 |
> |
system that had already formed double layers. These simulations then |
797 |
> |
had their CO molecules suddenly removed. The double layer broke apart |
798 |
> |
rapidly in these simulations, showing a well-defined edge-splitting |
799 |
> |
after 100~ps. Configurations of this system are shown in Figure |
800 |
> |
\ref{fig:breaking}. The coloring of the top and bottom layers helps to |
801 |
> |
show how much mixing the edges experience as they split. These systems |
802 |
> |
were only examined for 10~ns, and within that time despite the initial |
803 |
> |
rapid splitting, the edges only moved another few \AA~apart. It is |
804 |
> |
possible that with longer simulation times, the (557) surface recovery |
805 |
> |
observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered. |
806 |
|
|
542 |
– |
|
807 |
|
%breaking of the double layer upon removal of CO |
808 |
|
\begin{figure}[H] |
809 |
< |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
810 |
< |
\caption{Hi} |
809 |
> |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} |
810 |
> |
\caption{Behavior of an established (111) double step after removal of |
811 |
> |
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the |
812 |
> |
removal of CO. Nearly immediately after the CO is removed, the |
813 |
> |
step edge reforms in a (100) configuration, which is also the step |
814 |
> |
type seen on clean (557) surfaces. The step separation involves |
815 |
> |
significant mixing of the lower and upper atoms at the edge.} |
816 |
|
\label{fig:breaking} |
817 |
|
\end{figure} |
818 |
|
|
819 |
|
|
551 |
– |
|
552 |
– |
|
820 |
|
%Peaks! |
821 |
< |
\begin{figure}[H] |
822 |
< |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
823 |
< |
\caption{} |
824 |
< |
\label{fig:peaks} |
825 |
< |
\end{figure} |
821 |
> |
%\begin{figure}[H] |
822 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
823 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
824 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
825 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
826 |
> |
%\label{fig:peaks} |
827 |
> |
%\end{figure} |
828 |
|
|
829 |
+ |
|
830 |
+ |
%Don't think I need this |
831 |
|
%clean surface... |
832 |
< |
\begin{figure}[H] |
833 |
< |
\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
834 |
< |
\caption{} |
832 |
> |
%\begin{figure}[H] |
833 |
> |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF} |
834 |
> |
%\caption{} |
835 |
|
|
836 |
< |
\end{figure} |
837 |
< |
\label{fig:clean} |
836 |
> |
%\end{figure} |
837 |
> |
%\label{fig:clean} |
838 |
> |
|
839 |
> |
|
840 |
|
\section{Conclusion} |
841 |
+ |
The strength and directionality of the Pt-CO binding interaction, as |
842 |
+ |
well as the large quadrupolar repulsion between atop-bound CO |
843 |
+ |
molecules, help to explain the observed increase in surface mobility |
844 |
+ |
of Pt(557) and the resultant reconstruction into a double-layer |
845 |
+ |
configuration at the highest simulated CO-coverages. The weaker Au-CO |
846 |
+ |
interaction results in significantly lower adataom diffusion |
847 |
+ |
constants, less step-wandering, and a lack of the double layer |
848 |
+ |
reconstruction on the Au(557) surface. |
849 |
|
|
850 |
+ |
An in-depth examination of the energetics shows the important role CO |
851 |
+ |
plays in increasing step-breakup and in facilitating edge traversal |
852 |
+ |
which are both necessary for double layer formation. |
853 |
|
|
854 |
|
%Things I am not ready to remove yet |
855 |
|
|
873 |
|
% \end{tabular} |
874 |
|
% \end{table} |
875 |
|
|
876 |
< |
\section{Acknowledgments} |
877 |
< |
Support for this project was provided by the National Science |
878 |
< |
Foundation under grant CHE-0848243 and by the Center for Sustainable |
879 |
< |
Energy at Notre Dame (cSEND). Computational time was provided by the |
880 |
< |
Center for Research Computing (CRC) at the University of Notre Dame. |
881 |
< |
|
876 |
> |
\begin{acknowledgement} |
877 |
> |
We gratefully acknowledge conversations with Dr. William |
878 |
> |
F. Schneider and Dr. Feng Tao. Support for this project was |
879 |
> |
provided by the National Science Foundation under grant CHE-0848243 |
880 |
> |
and by the Center for Sustainable Energy at Notre Dame |
881 |
> |
(cSEND). Computational time was provided by the Center for Research |
882 |
> |
Computing (CRC) at the University of Notre Dame. |
883 |
> |
\end{acknowledgement} |
884 |
|
\newpage |
885 |
< |
\bibliography{firstTryBibliography} |
886 |
< |
\end{doublespace} |
885 |
> |
\bibstyle{achemso} |
886 |
> |
\bibliography{COonPtAu} |
887 |
> |
%\end{doublespace} |
888 |
> |
|
889 |
> |
\begin{tocentry} |
890 |
> |
\begin{wrapfigure}{l}{0.5\textwidth} |
891 |
> |
\begin{center} |
892 |
> |
\includegraphics[width=\linewidth]{TOC_doubleLayer} |
893 |
> |
\end{center} |
894 |
> |
\end{wrapfigure} |
895 |
> |
A reconstructed Pt(557) surface after 86~ns exposure to a half a |
896 |
> |
monolayer of CO. The double layer that forms is a result of |
897 |
> |
CO-mediated step-edge wandering as well as a burrowing mechanism that |
898 |
> |
helps lift edge atoms onto an upper terrace. |
899 |
> |
\end{tocentry} |
900 |
> |
|
901 |
|
\end{document} |