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\begin{document} |
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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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\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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\keywords{} |
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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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|
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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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% make the title |
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\maketitle |
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\begin{doublespace} |
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\begin{abstract} |
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|
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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. |
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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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This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557) |
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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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of the process are of particular interest, we employ 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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computational efficiency necessary to simulate the process of interest. |
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Since restructuring typically occurs as a result of specific interactions of the |
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catalyst with adsorbates, in this work, two metal systems exposed |
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to carbon monoxide were examined. The Pt(557) surface has already been shown |
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to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
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The Au(557) surface, because of a weaker interaction with CO, is less |
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likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000} |
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and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced |
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reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the |
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22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
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become adatoms, limiting the stress of this reconstruction, while |
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allowing the rest to relax and approach the ideal (111) |
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configuration. They did not see the usual herringbone pattern on Au(111) being greatly |
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affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a |
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disruption of the herringbone pattern as CO was adsorbed to the |
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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 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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|
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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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The challenge in modeling any solid/gas interface 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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10$^4$ atoms) 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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Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid |
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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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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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parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the |
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fastest of these density functional approaches. In |
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all of these models, atoms are treated 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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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} One of EAM's strengths |
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is its sensitivity to small changes in structure. This arises |
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because interactions |
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up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a} |
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Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88} |
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which is only parameterized up to the nearest-neighbor |
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interactions, EAM is a suitable choice for systems where |
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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 adsorbates somewhat easier. |
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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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Previous explanations for the surface rearrangements center on |
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the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} |
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We used a model first proposed by Karplus and Straub to study |
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the photodissociation of CO from myoglobin because it reproduces |
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the quadrupole moment well.\cite{Straub} The Straub and |
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Karplus model treats CO as a rigid three site molecule with a massless M |
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site at the molecular center of mass. The geometry and interaction |
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parameters are reproduced in Table~\ref{tab:CO}. 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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\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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interactions in 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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\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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|
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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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{\sc 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 |
261 |
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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 |
307 |
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performed until the energy difference between subsequent steps |
308 |
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was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
309 |
> |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
310 |
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zone.\cite{Monkhorst:1976} The relaxed gold slab was |
311 |
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then used in numerous single point calculations with CO at various |
312 |
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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 in this work are shown in Table 2 and the |
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binding energies on the 111 surfaces are displayed in Table 3. To |
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speed up the computations, charge transfer and polarization are not |
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being treated in this model, although these effects are likely to |
320 |
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affect binding energies and binding site |
278 |
< |
preferences.\cite{Deshlahra:2012} |
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> |
The parameters employed for the metal-CO cross-interactions in this work |
317 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
318 |
> |
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
319 |
> |
and polarization are neglected in this model, although these effects could have |
320 |
> |
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 |
324 |
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%Au Parameter Set 35 |
325 |
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\begin{table}[H] |
326 |
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\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
327 |
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interactions are modeled with Lennard-Jones potential, while the |
328 |
< |
(mostly-repulsive) metal-O interactions were fit to Morse |
326 |
> |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
327 |
> |
interactions are modeled with Lennard-Jones potentials. While the |
328 |
> |
metal-O interactions were fit to Morse |
329 |
|
potentials. Distances are given in \AA~and energies in kcal/mol. } |
330 |
|
\centering |
331 |
|
\begin{tabular}{| c | cc | c | ccc |} |
337 |
|
|
338 |
|
\hline |
339 |
|
\end{tabular} |
340 |
+ |
\label{tab:co_parameters} |
341 |
|
\end{table} |
342 |
|
|
343 |
|
%Table of energies |
344 |
|
\begin{table}[H] |
345 |
< |
\caption{Adsorption energies for CO on M(111) using the potentials |
346 |
< |
described in this work. All values are in eV} |
345 |
> |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
346 |
> |
described in this work. All values are in eV.} |
347 |
|
\centering |
348 |
|
\begin{tabular}{| c | cc |} |
349 |
|
\hline |
352 |
|
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
353 |
|
(Ref. \protect\cite{Kelemen:1979}) \\ |
354 |
|
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
355 |
< |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
355 |
> |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
356 |
|
\hline |
357 |
|
\end{tabular} |
358 |
+ |
\label{tab:co_energies} |
359 |
|
\end{table} |
360 |
|
|
361 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
362 |
< |
|
363 |
< |
Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a |
364 |
< |
FCC crystal that have been cut along the 557 plane so that they are |
365 |
< |
periodic in the {\it x} and {\it y} directions, and have been rotated |
366 |
< |
to expose two parallel 557 cuts along the positive and negative {\it |
367 |
< |
z}-axis. Simulations of the bare metal interfaces at temperatures |
368 |
< |
ranging from 300~K to 1200~K were done to observe the relative |
362 |
> |
Our Pt system is an orthorhombic periodic box of dimensions |
363 |
> |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
364 |
> |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
365 |
> |
are 9 and 8 atoms deep respectively, corresponding to a slab |
366 |
> |
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
367 |
> |
The systems are arranged in a FCC crystal that have been cut |
368 |
> |
along the (557) plane so that they are periodic in the {\it x} and |
369 |
> |
{\it y} directions, and have been oriented to expose two aligned |
370 |
> |
(557) cuts along the extended {\it z}-axis. Simulations of the |
371 |
> |
bare metal interfaces at temperatures ranging from 300~K to |
372 |
> |
1200~K were performed to confirm the relative |
373 |
|
stability of the surfaces without a CO overlayer. |
374 |
|
|
375 |
< |
The different bulk (and surface) melting temperatures (1337~K for Au |
376 |
< |
and 2045~K for Pt) suggest that the reconstruction may happen at |
377 |
< |
different temperatures for the two metals. To copy experimental |
330 |
< |
conditions for the CO-exposed surfaces, the bare surfaces were |
375 |
> |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
376 |
> |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
377 |
> |
different temperatures for the two metals. The bare Au and Pt surfaces were |
378 |
|
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
379 |
< |
respectively for 100 ps. Each surface was exposed to a range of CO |
379 |
> |
respectively for 100 ps. The two surfaces were relatively stable at these |
380 |
> |
temperatures when no CO was present, but experienced increased surface |
381 |
> |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
382 |
|
that was initially placed in the vacuum region. Upon full adsorption, |
383 |
< |
these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
384 |
< |
coverage. Because of the difference in binding energies, the platinum |
385 |
< |
systems very rarely had CO that was not bound to the surface, while |
386 |
< |
the gold surfaces often had a significant CO population in the gas |
383 |
> |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
384 |
> |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
385 |
> |
which introduces artifacts that are not relevant to (557) reconstruction. |
386 |
> |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
387 |
> |
the Au surfaces often had a significant CO population in the gas |
388 |
|
phase. These systems were allowed to reach thermal equilibrium (over |
389 |
< |
5 ns) before being shifted to the microcanonical (NVE) ensemble for |
390 |
< |
data collection. All of the systems examined had at least 40 ns in the |
391 |
< |
data collection stage, although simulation times for some of the |
392 |
< |
systems exceeded 200ns. All simulations were run using the open |
393 |
< |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD} |
389 |
> |
5~ns) before being run in the microcanonical (NVE) ensemble for |
390 |
> |
data collection. All of the systems examined had at least 40~ns in the |
391 |
> |
data collection stage, although simulation times for some Pt of the |
392 |
> |
systems exceeded 200~ns. Simulations were carried out using the open |
393 |
> |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,openmd} |
394 |
|
|
395 |
< |
% Just results, leave discussion for discussion section |
396 |
< |
% structure |
397 |
< |
% Pt: step wandering, double layers, no triangular motifs |
398 |
< |
% Au: step wandering, no double layers |
399 |
< |
% dynamics |
350 |
< |
% diffusion |
351 |
< |
% time scale, formation, breakage |
395 |
> |
|
396 |
> |
|
397 |
> |
|
398 |
> |
% RESULTS |
399 |
> |
% |
400 |
|
\section{Results} |
401 |
|
\subsection{Structural remodeling} |
402 |
< |
Tao {\it et al.} showed experimentally that the Pt(557) surface undergoes |
403 |
< |
two separate reconstructions upon CO adsorption.\cite{Tao:2010} The first |
404 |
< |
reconstruction involves a doubling of the step height and plateau length. Similar |
405 |
< |
behavior has been seen to occur on numerous surfaces at varying conditions.\cite{Williams:1994,Williams:1991,Pearl} |
406 |
< |
Of the two systems we examined, the Platinum system showed the most surface |
407 |
< |
reconstruction. Additionally, the amount of reconstruction appears to be |
408 |
< |
dependent on the amount of CO adsorbed upon the surface. This result is likely |
409 |
< |
related to the effect that coverage has on surface diffusion. While both systems |
410 |
< |
displayed step edge wandering, only the Pt surface underwent doubling within |
411 |
< |
the time scales we were modeling. Specifically only the 50 \% coverage Pt system |
412 |
< |
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. |
402 |
> |
The bare metal surfaces experienced minor roughening of the |
403 |
> |
step-edge because of the elevated temperatures, but the (557) |
404 |
> |
face was stable throughout the simulations. The surface of both |
405 |
> |
systems, upon dosage of CO, began to undergo extensive remodeling |
406 |
> |
that was not observed in the bare systems. Reconstructions of |
407 |
> |
the Au systems were limited to breakup of the step-edges and |
408 |
> |
some step wandering. The lower coverage Pt systems experienced |
409 |
> |
similar restructuring but to a greater extent. The 50\% coverage |
410 |
> |
Pt system was unique among our simulations in that it formed |
411 |
> |
well-defined and stable double layers through step coalescence, |
412 |
> |
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
413 |
|
|
372 |
– |
The second reconstruction on the Pt(557) surface observed by Tao involved the |
373 |
– |
formation of triangular clusters that stretched across the plateau between two step edges. |
374 |
– |
Neither system, within our simulated time scales, experiences this reconstruction. A constructed |
375 |
– |
system in which the triangular motifs were constructed on the surface will be explored in future |
376 |
– |
work and is shown in the supporting information. |
414 |
|
|
415 |
< |
\subsection{Dynamics} |
416 |
< |
While atomistic-like simulations of stepped surfaces have been performed before \cite{}, they tend to be |
417 |
< |
performed using Monte Carlo techniques\cite{Williams:1991,Williams:1994}. This allows them to efficiently sample the thermodynamic |
418 |
< |
landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM \cite{Pearl}, |
419 |
< |
has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition, ~ 70 s/image |
420 |
< |
provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments |
421 |
< |
of step edges are adept at analyzing such systems, it is important to remember that the edges are made |
422 |
< |
up of individual atoms and thus can be examined in numerous ways. |
415 |
> |
\subsubsection{Step wandering} |
416 |
> |
The 0\% coverage surfaces for both metals showed minimal |
417 |
> |
step-wandering at their respective temperatures. As the CO |
418 |
> |
coverage increased however, the mobility of the surface atoms, |
419 |
> |
described through adatom diffusion and step-edge wandering, |
420 |
> |
also increased. Except for the 50\% Pt system where step |
421 |
> |
coalescence occurred, the step-edges in the other simulations |
422 |
> |
preferred to keep nearly the same distance between steps as in |
423 |
> |
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
424 |
> |
Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
425 |
> |
highlights the repulsion that exists between step-edges even |
426 |
> |
when no direct interactions are present in the system. This |
427 |
> |
repulsion is caused by an entropic barrier that arises from |
428 |
> |
the fact that steps cannot cross over one another. This entropic |
429 |
> |
repulsion does not completely define the interactions between |
430 |
> |
steps, however, so it is possible to observe step coalescence |
431 |
> |
on some surfaces.\cite{Williams:1991} The presence and |
432 |
> |
concentration of adsorbates, as shown in this work, can |
433 |
> |
affect step-step interactions, potentially leading to a new |
434 |
> |
surface structure as the thermodynamic equilibrium. |
435 |
|
|
436 |
< |
\subsubsection{Transport of surface metal atoms} |
437 |
< |
%forcedSystems/stepSeparation |
438 |
< |
The movement of a step edge is a cooperative effect arising from the individual movements of the atoms |
439 |
< |
making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to |
440 |
< |
experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface. |
441 |
< |
For our surfaces however, the presence of step edges provide a source for mobile metal atoms. Breaking away |
442 |
< |
from the step edge still imposes an energetic penalty around 40 kcal/mole, but is much less than lifting the same metal |
443 |
< |
atom out from the surface, > 60 kcal/mole, and the penalty lowers even further when CO is present in sufficient quantities |
444 |
< |
on the surface, ~20 kcal/mole. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole) |
445 |
< |
and is well able to explore its terrace. Atoms traversing terraces is more difficult, but can be overcome through a joining and lifting stage. |
446 |
< |
By tracking the mobility of individual metal atoms on the Platinum and Gold surfaces we were able to determine |
447 |
< |
the relative diffusion rates and how varying coverages of CO affected the rates. Close |
448 |
< |
observation of the mobile metal atoms showed that they were typically in equilibrium with the |
449 |
< |
step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and |
450 |
< |
two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying |
451 |
< |
the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
436 |
> |
\subsubsection{Double layers} |
437 |
> |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
438 |
> |
undergoes two separate reconstructions upon CO adsorption. |
439 |
> |
The first involves a doubling of the step height and plateau length. |
440 |
> |
Similar behavior has been seen on a number of surfaces |
441 |
> |
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
442 |
> |
Of the two systems we examined, the Pt system showed a greater |
443 |
> |
propensity for reconstruction |
444 |
> |
because of the larger surface mobility and the greater extent of step wandering. |
445 |
> |
The amount of reconstruction was strongly correlated to the amount of CO |
446 |
> |
adsorbed upon the surface. This appears to be related to the |
447 |
> |
effect that adsorbate coverage has on edge breakup and on the |
448 |
> |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
449 |
> |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
450 |
> |
Over a longer time scale (150~ns) two more double layers formed |
451 |
> |
on this surface. Although double layer formation did not occur |
452 |
> |
in the other Pt systems, they exhibited more step-wandering and |
453 |
> |
roughening compared to their Au counterparts. The |
454 |
> |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
455 |
> |
various times along the simulation showing the evolution of a double layer step-edge. |
456 |
|
|
457 |
< |
A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations |
458 |
< |
of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but |
459 |
< |
the 2~\AA~ cutoff was to prevent the in-place vibrational movement of atoms from being included in the analysis. |
460 |
< |
Since diffusion on a surface is strongly affected by local structures, in this case the presence of single and double |
461 |
< |
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}. |
457 |
> |
The second reconstruction observed by |
458 |
> |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
459 |
> |
across the plateau between two step-edges. Neither metal, within |
460 |
> |
the 40~ns time scale or the extended simulation time of 150~ns for |
461 |
> |
the 50\% Pt system, experienced this reconstruction. |
462 |
|
|
411 |
– |
\subsubsection{Double layer formation} |
412 |
– |
The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the |
413 |
– |
formation of double layers, seeing as how that was the only system within our observed simulation time |
414 |
– |
that showed the formation. Despite this being the only system where this reconstruction occurs, three separate layers |
415 |
– |
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. |
423 |
– |
|
463 |
|
%Evolution of surface |
464 |
|
\begin{figure}[H] |
465 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
465 |
> |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} |
466 |
|
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
467 |
< |
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
468 |
< |
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
469 |
< |
doubling of the layers appears only after two adjacent step edges |
467 |
> |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
468 |
> |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
469 |
> |
doubling of the layers appears only after two adjacent step-edges |
470 |
|
touch. The circled spot in (b) nucleated the growth of the double |
471 |
|
step observed in the later configurations.} |
472 |
|
\label{fig:reconstruct} |
473 |
|
\end{figure} |
474 |
|
|
475 |
+ |
\subsection{Dynamics} |
476 |
+ |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
477 |
+ |
using STM, has been able to capture the coalescence of steps |
478 |
+ |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
479 |
+ |
provides an upper bound for the time required for the doubling |
480 |
+ |
to occur. By utilizing Molecular Dynamics we are able to probe |
481 |
+ |
the dynamics of these reconstructions at elevated temperatures |
482 |
+ |
and in this section we provide data on the timescales for transport |
483 |
+ |
properties, e.g. diffusion and layer formation time. |
484 |
+ |
|
485 |
+ |
|
486 |
+ |
\subsubsection{Transport of surface metal atoms} |
487 |
+ |
%forcedSystems/stepSeparation |
488 |
+ |
The wandering of a step-edge is a cooperative effect |
489 |
+ |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
490 |
+ |
displaying a low index facet, (111) or (100), is unlikely to experience |
491 |
+ |
much surface diffusion because of the large energetic barrier that must |
492 |
+ |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
493 |
+ |
on higher-index facets provides a lower energy source for mobile metal atoms. |
494 |
+ |
Single-atom break-away from a step-edge on a clean surface still imposes an |
495 |
+ |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
496 |
+ |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
497 |
+ |
The penalty lowers significantly when CO is present in sufficient quantities |
498 |
+ |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
499 |
+ |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
500 |
+ |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
501 |
+ |
able to explore the terrace before rejoining either their original step-edge or |
502 |
+ |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
503 |
+ |
to traverse to a separate terrace although the presence of CO can lower the |
504 |
+ |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
505 |
+ |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
506 |
+ |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
507 |
+ |
observation of the mobile metal atoms showed that they were typically in |
508 |
+ |
equilibrium with the step-edges. |
509 |
+ |
At times, their motion was concerted and two or more adatoms would be |
510 |
+ |
observed moving together across the surfaces. |
511 |
+ |
|
512 |
+ |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
513 |
+ |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
514 |
+ |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
515 |
+ |
was used to prevent swamping the diffusion data with the in-place vibrational |
516 |
+ |
movement of buried atoms. Diffusion on a surface is strongly affected by |
517 |
+ |
local structures and in this work, the presence of single and double layer |
518 |
+ |
step-edges causes the diffusion parallel to the step-edges to be larger than |
519 |
+ |
the diffusion perpendicular to these edges. Parallel and perpendicular |
520 |
+ |
diffusion constants are shown in Figure \ref{fig:diff}. |
521 |
+ |
|
522 |
+ |
%Diffusion graph |
523 |
|
\begin{figure}[H] |
524 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
524 |
> |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1} |
525 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
526 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
527 |
< |
($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO |
528 |
< |
surface coverage. Diffusion parallel to the step edge is higher |
527 |
> |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
528 |
> |
surface coverage. Diffusion parallel to the step-edge is higher |
529 |
|
than that perpendicular to the edge because of the lower energy |
530 |
< |
barrier associated with going from approximately 7 nearest neighbors |
531 |
< |
to 5, as compared to the 3 of an adatom. Additionally, the observed |
532 |
< |
maximum and subsequent decrease for the Pt system suggests that the |
533 |
< |
CO self-interactions are playing a significant role with regards to |
534 |
< |
movement of the platinum atoms around and more importantly across |
448 |
< |
the surface. } |
530 |
> |
barrier associated with traversing along the edge as compared to |
531 |
> |
completely breaking away. The two reported diffusion constants for |
532 |
> |
the 50\% Pt system arise from different sample sets. The lower values |
533 |
> |
correspond to the same 40~ns amount that all of the other systems were |
534 |
> |
examined at, while the larger values correspond to a 20~ns period } |
535 |
|
\label{fig:diff} |
536 |
|
\end{figure} |
537 |
|
|
538 |
+ |
The weaker Au-CO interaction is evident in the weak CO-coverage |
539 |
+ |
dependance of Au diffusion. This weak interaction leads to lower |
540 |
+ |
observed coverages when compared to dosage amounts. This further |
541 |
+ |
limits the effect the CO can have on surface diffusion. The correlation |
542 |
+ |
between coverage and Pt diffusion rates shows a near linear relationship |
543 |
+ |
at the earliest times in the simulations. Following double layer formation, |
544 |
+ |
however, there is a precipitous drop in adatom diffusion. As the double |
545 |
+ |
layer forms, many atoms that had been tracked for mobility data have |
546 |
+ |
now been buried resulting in a smaller reported diffusion constant. A |
547 |
+ |
secondary effect of higher coverages is CO-CO cross interactions that |
548 |
+ |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
549 |
+ |
This effect would become evident only at higher coverages. A detailed |
550 |
+ |
account of Pt adatom energetics follows in the Discussion. |
551 |
+ |
|
552 |
|
|
553 |
+ |
\subsubsection{Dynamics of double layer formation} |
554 |
+ |
The increased diffusion on Pt at the higher CO coverages is the primary |
555 |
+ |
contributor to double layer formation. However, this is not a complete |
556 |
+ |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
557 |
+ |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
558 |
+ |
system, one double layer formed within the first 40~ns of simulation time, |
559 |
+ |
while two more were formed as the system was allowed to run for an |
560 |
+ |
additional 110~ns (150~ns total). This suggests that this reconstruction |
561 |
+ |
is a rapid process and that the previously mentioned upper bound is a |
562 |
+ |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
563 |
+ |
appearance of a double layer appears at 19~ns into the simulation. |
564 |
+ |
Within 12~ns of this nucleation event, nearly half of the step has formed |
565 |
+ |
the double layer and by 86~ns the complete layer has flattened out. |
566 |
+ |
From the appearance of the first nucleation event to the first observed |
567 |
+ |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
568 |
+ |
necessary for the layer to completely straighten. The other two layers in |
569 |
+ |
this simulation formed over periods of 22~ns and 42~ns respectively. |
570 |
+ |
A possible explanation for this rapid reconstruction is the elevated |
571 |
+ |
temperatures under which our systems were simulated. The process |
572 |
+ |
would almost certainly take longer at lower temperatures. Additionally, |
573 |
+ |
our measured times for completion of the doubling after the appearance |
574 |
+ |
of a nucleation site are likely affected by our periodic boxes. A longer |
575 |
+ |
step-edge will likely take longer to ``zipper''. |
576 |
|
|
577 |
|
|
578 |
|
%Discussion |
579 |
|
\section{Discussion} |
580 |
< |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
581 |
< |
Pt (557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
582 |
< |
were able to capture the dynamic processes inherent within this reconstruction. |
580 |
> |
We have shown that a classical potential is able to model the initial |
581 |
> |
reconstruction of the Pt(557) surface upon CO adsorption, and have |
582 |
> |
reproduced the double layer structure observed by Tao {\it et |
583 |
> |
al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be |
584 |
> |
rapid -- occurring within 100 ns of the initial exposure to CO. Here |
585 |
> |
we discuss the features of the classical potential that are |
586 |
> |
contributing to the stability and speed of the Pt(557) reconstruction. |
587 |
|
|
588 |
< |
\subsection{Mechanism for restructuring} |
589 |
< |
The increased computational cost to examine this system using molecular dynamics rather than |
590 |
< |
a Monte Carlo based approach was necessary so that our predictions on possible mechanisms |
591 |
< |
and driving forces would have support not only from thermodynamic arguments but also from the |
592 |
< |
actual dynamics of the system. |
588 |
> |
\subsection{Diffusion} |
589 |
> |
The perpendicular diffusion constant appears to be the most important |
590 |
> |
indicator of double layer formation. As highlighted in Figure |
591 |
> |
\ref{fig:reconstruct}, the formation of the double layer did not begin |
592 |
> |
until a nucleation site appeared. Williams {\it et |
593 |
> |
al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge |
594 |
> |
repulsion arising from the inability of edge crossing. This repulsion |
595 |
> |
must be overcome to allow step coalescence. A larger |
596 |
> |
$\textbf{D}_\perp$ value implies more step-wandering and a larger |
597 |
> |
chance for the stochastic meeting of two edges to create a nucleation |
598 |
> |
point. Diffusion parallel to the step-edge can help ``zipper'' up a |
599 |
> |
nascent double layer. This helps explain the rapid time scale for |
600 |
> |
double layer completion after the appearance of a nucleation site, while |
601 |
> |
the initial appearance of the nucleation site was unpredictable. |
602 |
|
|
603 |
< |
Comparing the results from simulation to those reported previously by |
604 |
< |
Tao et al. the similarities in the platinum and CO system are quite |
605 |
< |
strong. As shown in figure \ref{fig:reconstruct}, the simulated platinum system under a CO |
606 |
< |
atmosphere will restructure slightly by doubling the terrace |
607 |
< |
heights. The restructuring appears to occur slowly, one to two |
608 |
< |
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 |
603 |
> |
\subsection{Mechanism for restructuring} |
604 |
> |
Since the Au surface showed no large scale restructuring in any of our |
605 |
> |
simulations, our discussion will focus on the 50\% Pt-CO system which |
606 |
> |
did exhibit doubling. A number of possible mechanisms exist to explain |
607 |
> |
the role of adsorbed CO in restructuring the Pt surface. Quadrupolar |
608 |
> |
repulsion between adjacent CO molecules adsorbed on the surface is one |
609 |
|
possibility. However, the quadrupole-quadrupole interaction is |
610 |
|
short-ranged and is attractive for some orientations. If the CO |
611 |
< |
molecules are ``locked'' in a specific orientation relative to each other however, |
612 |
< |
this explanation gains some weight. The energetic repulsion between two CO |
613 |
< |
located a distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in a |
614 |
< |
vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second nearest-neighbor |
615 |
< |
distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to nearly 0 kcal/mole. SHOW A NUMBER FOR ROTATION. |
616 |
< |
As mentioned above, the energy barrier for surface diffusion of a platinum adatom is only 4 kcal/mole. So this |
617 |
< |
repulsion between CO can help increase the surface diffusion. However, the residence time of CO was examined |
618 |
< |
and while the majority of the CO is on or near the surface throughout the run, it is extremely mobile. This mobility |
619 |
< |
suggests that the CO are more likely to shift their positions without necessarily dragging the platinum along |
620 |
< |
with them. |
611 |
> |
molecules are ``locked'' in a vertical orientation, through atop |
612 |
> |
adsorption for example, this explanation would gain credence. The |
613 |
> |
calculated energetic repulsion between two CO molecules located a |
614 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both |
615 |
> |
in a vertical orientation, is 8.62 kcal/mol. Moving the CO to the |
616 |
> |
second nearest-neighbor distance of 4.8~\AA~drops the repulsion to |
617 |
> |
nearly 0. Allowing the CO to rotate away from a purely vertical |
618 |
> |
orientation also lowers the repulsion. When the carbons are locked at |
619 |
> |
a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the |
620 |
> |
angle between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
621 |
> |
barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
622 |
> |
repulsion between adjacent CO molecules bound to Pt could increase the |
623 |
> |
surface diffusion. However, the residence time of CO on Pt suggests |
624 |
> |
that the CO molecules are extremely mobile, with diffusion constants 40 |
625 |
> |
to 2500 times larger than surface Pt atoms. This mobility suggests |
626 |
> |
that the CO molecules jump between different Pt atoms throughout the |
627 |
> |
simulation, but can stay bound for significant periods of time. |
628 |
|
|
629 |
< |
Another possible and more likely mechanism for the restructuring is in the |
630 |
< |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
631 |
< |
Pt atoms. This could have the effect of increasing surface mobility |
632 |
< |
of these atoms. To test this hypothesis, numerous configurations of |
633 |
< |
CO in varying quantities were arranged on the higher and lower plateaus |
634 |
< |
around a step on a otherwise clean Pt (557) surface. One representative |
635 |
< |
configuration is displayed in figure \ref{fig:lambda}. Single or concerted movement |
636 |
< |
of platinum atoms was then examined to determine possible barriers. Because |
637 |
< |
of the forced movement along a pre-defined reaction coordinate that may differ |
638 |
< |
from the true minimum of this path, only the beginning and ending energies |
639 |
< |
are displayed in table \ref{tab:energies}. The presence of CO at suitable |
640 |
< |
sites can lead to lowered barriers for platinum breaking apart from the step edge. |
641 |
< |
Additionally, as highlighted in figure \ref{fig:lambda}, the presence of CO makes the |
642 |
< |
burrowing and lifting nature favorable, whereas without CO, the process is neutral |
643 |
< |
in terms of energetics. |
629 |
> |
A different interpretation of the above mechanism which takes the |
630 |
> |
large mobility of the CO into account, would be in the destabilization |
631 |
> |
of Pt-Pt interactions due to bound CO. Destabilizing Pt-Pt bonds at |
632 |
> |
the edges could lead to increased step-edge breakup and diffusion. On |
633 |
> |
the bare Pt(557) surface the barrier to completely detach an edge atom |
634 |
> |
is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
635 |
> |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain |
636 |
> |
configurations, cases (e), (g), and (h), the barrier can be lowered to |
637 |
> |
$\sim$23~kcal/mol by the presence of bound CO molecules. In these |
638 |
> |
instances, it becomes energetically favorable to roughen the edge by |
639 |
> |
introducing a small separation of 0.5 to 1.0~\AA. This roughening |
640 |
> |
becomes immediately obvious in simulations with significant CO |
641 |
> |
populations. The roughening is present to a lesser extent on surfaces |
642 |
> |
with lower CO coverage (and even on the bare surfaces), although in |
643 |
> |
these cases it is likely due to random fluctuations that squeeze out |
644 |
> |
step-edge atoms. Step-edge breakup by continuous single-atom |
645 |
> |
translations (as suggested by these energy curves) is probably a |
646 |
> |
worst-case scenario. Multistep mechanisms in which an adatom moves |
647 |
> |
laterally on the surface after being ejected would be more |
648 |
> |
energetically favorable. This would leave the adatom alongside the |
649 |
> |
ledge, providing it with 5 nearest neighbors. While fewer than the 7 |
650 |
> |
neighbors it had as part of the step-edge, it keeps more Pt neighbors |
651 |
> |
than the 3 an isolated adatom would have on the terrace. In this |
652 |
> |
proposed mechanism, the CO quadrupolar repulsion still plays a role in |
653 |
> |
the initial roughening of the step-edge, but not in any long-term |
654 |
> |
bonds with individual Pt atoms. Higher CO coverages create more |
655 |
> |
opportunities for the crowded CO configurations shown in Figure |
656 |
> |
\ref{fig:SketchGraphic}, and this is likely to cause an increased |
657 |
> |
propensity for step-edge breakup. |
658 |
|
|
659 |
+ |
%Sketch graphic of different configurations |
660 |
+ |
\begin{figure}[H] |
661 |
+ |
\includegraphics[width=\linewidth]{COpaths} |
662 |
+ |
\caption{Configurations used to investigate the mechanism of step-edge |
663 |
+ |
breakup on Pt(557). In each case, the central (starred) atom is |
664 |
+ |
pulled directly across the surface away from the step edge. The Pt |
665 |
+ |
atoms on the upper terrace are colored dark grey, while those on the |
666 |
+ |
lower terrace are in white. In each of these configurations, some |
667 |
+ |
number of the atoms (highlighted in blue) had a CO molecule bound in |
668 |
+ |
a vertical atop position. The energies of these configurations as a |
669 |
+ |
function of central atom displacement are displayed in Figure |
670 |
+ |
\ref{fig:SketchEnergies}.} |
671 |
+ |
\label{fig:SketchGraphic} |
672 |
+ |
\end{figure} |
673 |
+ |
|
674 |
+ |
%energy graph corresponding to sketch graphic |
675 |
+ |
\begin{figure}[H] |
676 |
+ |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison} |
677 |
+ |
\caption{Energies for displacing a single edge atom perpendicular to |
678 |
+ |
the step edge as a function of atomic displacement. Each of the |
679 |
+ |
energy curves corresponds to one of the labeled configurations in |
680 |
+ |
Figure \ref{fig:SketchGraphic}, and are referenced to the |
681 |
+ |
unperturbed step-edge. Certain arrangements of bound CO (notably |
682 |
+ |
configurations g and h) can lower the energetic barrier for creating |
683 |
+ |
an adatom relative to the bare surface (configuration a).} |
684 |
+ |
\label{fig:SketchEnergies} |
685 |
+ |
\end{figure} |
686 |
+ |
|
687 |
+ |
While configurations of CO on the surface are able to increase |
688 |
+ |
diffusion and the likelihood of edge wandering, this does not provide |
689 |
+ |
a complete explanation for the formation of double layers. If adatoms |
690 |
+ |
were constrained to their original terraces then doubling could not |
691 |
+ |
occur. A mechanism for vertical displacement of adatoms at the |
692 |
+ |
step-edge is required to explain the doubling. |
693 |
+ |
|
694 |
+ |
We have discovered one possible mechanism for a CO-mediated vertical |
695 |
+ |
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} |
696 |
+ |
shows four points along a reaction coordinate in which a CO-bound |
697 |
+ |
adatom along the step-edge ``burrows'' into the edge and displaces the |
698 |
+ |
original edge atom onto the higher terrace. A number of events similar |
699 |
+ |
to this mechanism were observed during the simulations. We predict an |
700 |
+ |
energetic barrier of 20~kcal/mol for this process (in which the |
701 |
+ |
displaced edge atom follows a curvilinear path into an adjacent 3-fold |
702 |
+ |
hollow site). The barrier heights we obtain for this reaction |
703 |
+ |
coordinate are approximate because the exact path is unknown, but the |
704 |
+ |
calculated energy barriers would be easily accessible at operating |
705 |
+ |
conditions. Additionally, this mechanism is exothermic, with a final |
706 |
+ |
energy 15~kcal/mol below the original $\lambda = 0$ configuration. |
707 |
+ |
When CO is not present and this reaction coordinate is followed, the |
708 |
+ |
process is endothermic by 3~kcal/mol. The difference in the relative |
709 |
+ |
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present |
710 |
+ |
provides strong support for CO-mediated Pt-Pt interactions giving rise |
711 |
+ |
to the doubling reconstruction. |
712 |
+ |
|
713 |
|
%lambda progression of Pt -> shoving its way into the step |
714 |
|
\begin{figure}[H] |
715 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
716 |
< |
\caption{A model system of the Pt 557 surface was used as the framework for a reaction coordinate. |
717 |
< |
Various numbers, placements, and rotations of CO were examined. The one displayed was a |
718 |
< |
representative sample. As shown in Table , relative to the energy at 0\% there is a slight decrease |
719 |
< |
upon insertion of the platinum atom into the step edge along with the resultant lifting of the other |
720 |
< |
platinum atom.} |
715 |
> |
\includegraphics[width=\linewidth]{EPS_rxnCoord} |
716 |
> |
\caption{Points along a possible reaction coordinate for CO-mediated |
717 |
> |
edge doubling. Here, a CO-bound adatom burrows into an established |
718 |
> |
step edge and displaces an edge atom onto the upper terrace along a |
719 |
> |
curvilinear path. The approximate barrier for the process is |
720 |
> |
20~kcal/mol, and the complete process is exothermic by 15~kcal/mol |
721 |
> |
in the presence of CO, but is endothermic by 3~kcal/mol without.} |
722 |
|
\label{fig:lambda} |
723 |
|
\end{figure} |
724 |
|
|
725 |
+ |
The mechanism for doubling on the Pt(557) surface appears to require |
726 |
+ |
the cooperation of at least two distinct processes. For complete |
727 |
+ |
doubling of a layer to occur there must be a breakup of one |
728 |
+ |
terrace. These atoms must then ``disappear'' from that terrace, either |
729 |
+ |
by travelling to the terraces above of below their original levels. |
730 |
+ |
The presence of CO helps explain mechanisms for both of these |
731 |
+ |
situations. There must be sufficient breakage of the step-edge to |
732 |
+ |
increase the concentration of adatoms on the surface and these adatoms |
733 |
+ |
must then undergo the burrowing highlighted above (or a comparable |
734 |
+ |
mechanism) to create the double layer. With sufficient time, these |
735 |
+ |
mechanisms working in concert lead to the formation of a double layer. |
736 |
|
|
737 |
+ |
\subsection{CO Removal and double layer stability} |
738 |
+ |
Once a double layer had formed on the 50\%~Pt system, it remained for |
739 |
+ |
the rest of the simulation time with minimal movement. Random |
740 |
+ |
fluctuations that involved small clusters or divots were observed, but |
741 |
+ |
these features typically healed within a few nanoseconds. Within our |
742 |
+ |
simulations, the formation of the double layer appeared to be |
743 |
+ |
irreversible and a double layer was never observed to split back into |
744 |
+ |
two single layer step-edges while CO was present. |
745 |
|
|
746 |
< |
\subsection{Diffusion} |
747 |
< |
As shown in the results section, the diffusion parallel to the step edge tends to be |
748 |
< |
much faster than that perpendicular to the step edge. Additionally, the coverage |
749 |
< |
of CO appears to play a slight role in relative rates of diffusion, as shown in figure \ref{fig:diff} |
750 |
< |
Thus, the bottleneck of the double layer formation appears to be the initial formation |
751 |
< |
of this growth point, which seems to be somewhat of a stochastic event. Once it |
752 |
< |
appears, parallel diffusion, along the now slightly angled step edge, will allow for |
753 |
< |
a faster formation of the double layer than if the entire process were dependent on |
754 |
< |
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
755 |
< |
more likely a growth point is to be formed. |
756 |
< |
\\ |
746 |
> |
To further gauge the effect CO has on this surface, additional |
747 |
> |
simulations were run starting from a late configuration of the 50\%~Pt |
748 |
> |
system that had already formed double layers. These simulations then |
749 |
> |
had their CO forcibly removed. The double layer broke apart rapidly |
750 |
> |
in these simulations, showing a well-defined edge-splitting after |
751 |
> |
100~ps. Configurations of this system are shown in Figure |
752 |
> |
\ref{fig:breaking}. The coloring of the top and bottom layers helps to |
753 |
> |
exhibit how much mixing the edges experience as they split. These |
754 |
> |
systems were only examined for 10~ns, and within that time despite the |
755 |
> |
initial rapid splitting, the edges only moved another few |
756 |
> |
\AA~apart. It is possible that with longer simulation times, the (557) |
757 |
> |
surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could |
758 |
> |
also be recovered. |
759 |
|
|
542 |
– |
|
760 |
|
%breaking of the double layer upon removal of CO |
761 |
|
\begin{figure}[H] |
762 |
< |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
763 |
< |
\caption{Hi} |
762 |
> |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} |
763 |
> |
\caption{Dynamics of an established (111) double step after removal of |
764 |
> |
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal |
765 |
> |
of CO. The presence of the CO helped maintain the stability of the |
766 |
> |
double step. Nearly immediately after the CO is removed, the step |
767 |
> |
edge reforms in a (100) configuration, which is also the step type |
768 |
> |
seen on clean (557) surfaces. The step separation involves |
769 |
> |
significant mixing of the lower and upper atoms at the edge.} |
770 |
|
\label{fig:breaking} |
771 |
|
\end{figure} |
772 |
|
|
773 |
|
|
551 |
– |
|
552 |
– |
|
774 |
|
%Peaks! |
775 |
< |
\begin{figure}[H] |
776 |
< |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
777 |
< |
\caption{} |
778 |
< |
\label{fig:peaks} |
779 |
< |
\end{figure} |
775 |
> |
%\begin{figure}[H] |
776 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
777 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
778 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
779 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
780 |
> |
%\label{fig:peaks} |
781 |
> |
%\end{figure} |
782 |
|
|
783 |
+ |
|
784 |
+ |
%Don't think I need this |
785 |
|
%clean surface... |
786 |
< |
\begin{figure}[H] |
787 |
< |
\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
788 |
< |
\caption{} |
786 |
> |
%\begin{figure}[H] |
787 |
> |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF} |
788 |
> |
%\caption{} |
789 |
|
|
790 |
< |
\end{figure} |
791 |
< |
\label{fig:clean} |
790 |
> |
%\end{figure} |
791 |
> |
%\label{fig:clean} |
792 |
> |
|
793 |
> |
|
794 |
|
\section{Conclusion} |
795 |
+ |
The strength and directionality of the Pt-CO binding interaction, as |
796 |
+ |
well as the large quadrupolar repulsion between atop-bound CO |
797 |
+ |
molecules, help to explain the observed increase in surface mobility |
798 |
+ |
of Pt(557) and the resultant reconstruction into a double-layer |
799 |
+ |
configuration at the highest simulated CO-coverages. The weaker Au-CO |
800 |
+ |
interaction results in significantly lower adataom diffusion |
801 |
+ |
constants, less step-wandering, and a lack of the double layer |
802 |
+ |
reconstruction on the Au(557) surface. |
803 |
|
|
804 |
+ |
An in-depth examination of the energetics shows the important role CO |
805 |
+ |
plays in increasing step-breakup and in facilitating edge traversal |
806 |
+ |
which are both necessary for double layer formation. |
807 |
|
|
808 |
|
%Things I am not ready to remove yet |
809 |
|
|
827 |
|
% \end{tabular} |
828 |
|
% \end{table} |
829 |
|
|
830 |
< |
\section{Acknowledgments} |
831 |
< |
Support for this project was provided by the National Science |
832 |
< |
Foundation under grant CHE-0848243 and by the Center for Sustainable |
833 |
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Energy at Notre Dame (cSEND). Computational time was provided by the |
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Center for Research Computing (CRC) at the University of Notre Dame. |
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|
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\begin{acknowledgement} |
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We gratefully acknowledge conversations with Dr. William |
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F. Schneider and Dr. Feng Tao. Support for this project was |
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provided by the National Science Foundation under grant CHE-0848243 |
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and by the Center for Sustainable Energy at Notre Dame |
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(cSEND). Computational time was provided by the Center for Research |
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Computing (CRC) at the University of Notre Dame. |
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\end{acknowledgement} |
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\newpage |
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\bibliography{firstTryBibliography} |
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\end{doublespace} |
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%\end{doublespace} |
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|
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\begin{tocentry} |
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|
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\includegraphics[height=2.8cm]{TOC_doubleLayer} |
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|
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A reconstructed Pt(557) surface after having been exposed to a dosage of CO equivalent to half a monolayer of coverage. |
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|
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\end{tocentry} |
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|
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\end{document} |