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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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\begin{abstract} |
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We examine surface reconstructions of Pt and Au(557) under |
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various CO coverages using molecular dynamics in order to |
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explore possible mechanisms for any observed reconstructions |
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and their dynamics. The metal-CO interactions were parameterized |
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as part of this work so that an efficient large-scale treatment of |
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this system could be undertaken. The large difference in binding |
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strengths of the metal-CO interactions was found to play a significant |
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role with regards to step-edge stability and adatom diffusion. A |
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small correlation between coverage and the diffusion constant |
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was also determined. The energetics of CO adsorbed to the surface |
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is sufficient to explain the reconstructions observed on the Pt |
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systems and the lack of reconstruction of the Au systems. |
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|
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|
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The mechanism and dynamics of surface reconstructions of Pt(557) |
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and Au(557) exposed to various coverages of carbon monoxide (CO) |
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were investigated using molecular dynamics simulations. Metal-CO |
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interactions were parameterized from experimental data and plane-wave |
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Density Functional Theory (DFT) calculations. The large difference in |
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binding strengths of the Pt-CO and Au-CO interactions was found to play |
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a significant role in step-edge stability and adatom diffusion constants. |
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The energetics of CO adsorbed to the surface is sufficient to explain the |
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step-doubling reconstruction observed on Pt(557) and the lack of such |
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a reconstruction on the Au(557) surface. |
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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 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 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 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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|
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This work is an investigation into the mechanism and timescale for the |
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Pt(557) \& Au(557) surface restructuring using molecular simulation. |
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Since the dynamics of the process are of particular interest, we |
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employ classical force fields that represent a compromise between |
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chemical accuracy and the computational efficiency necessary to |
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simulate the process of interest. Since restructuring typically |
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occurs as a result of specific interactions of the catalyst with |
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adsorbates, in this work, two metal systems exposed to carbon monoxide |
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were examined. The Pt(557) surface has already been shown to undergo a |
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large scale reconstruction under certain conditions.\cite{Tao:2010} |
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The Au(557) surface, because of weaker interactions with CO, is less |
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likely to undergo this kind of reconstruction. However, Peters {\it et |
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al}.\cite{Peters:2000} and Piccolo {\it et al}.\cite{Piccolo:2004} |
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have both observed CO-induced modification of reconstructions to the |
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Au(111) surface. Peters {\it et al}. observed the Au(111)-($22 \times |
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\sqrt{3}$) ``herringbone'' reconstruction relaxing slightly under CO |
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adsorption. They argued that only a few Au atoms become adatoms, |
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limiting the stress of this reconstruction, while allowing the rest to |
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relax and approach the ideal (111) configuration. Piccolo {\it et |
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al}. on the other hand, saw a more significant disruption of the |
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Au(111)-($22 \times \sqrt{3}$) herringbone pattern as CO adsorbed on |
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the surface. Both groups suggested that the preference CO shows for |
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low-coordinated Au atoms was the primary driving force for the |
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relaxation. Although the Au(111) reconstruction was not the primary |
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goal of our work, the classical models we have fit may be of future |
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use in simulating this reconstruction. |
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|
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%Platinum molecular dynamics |
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%gold molecular dynamics |
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\section{Simulation Methods} |
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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$^4$ 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.\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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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}.\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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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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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} 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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\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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\subsection{Carbon Monoxide model} |
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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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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 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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$\epsilon$), 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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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 were |
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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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are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
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(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
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and polarization are neglected in this model, although these effects could have |
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an effect on binding energies and binding site preferences. |
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an effect on binding energies and binding site preferences. |
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|
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%Table of Parameters |
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%Pt Parameter Set 9 |
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%Au Parameter Set 35 |
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\begin{table}[H] |
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\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
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interactions are modeled with Lennard-Jones potentials. While the |
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metal-O interactions were fit to Morse |
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\caption{Parameters for the metal-CO cross-interactions. Metal-C |
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interactions are modeled with Lennard-Jones potentials, while the |
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metal-O interactions were fit to broad Morse |
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potentials. Distances are given in \AA~and energies in kcal/mol. } |
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\centering |
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\begin{tabular}{| c | cc | c | ccc |} |
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\hline |
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\end{tabular} |
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\label{tab:co_energies} |
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\end{table} |
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|
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|
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\subsection{Validation of forcefield selections} |
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By calculating minimum energies for commensurate systems of |
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single and double layer Pt and Au systems with 0 and 50\% coverages |
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(arranged in a c(2x4) pattern), our forcefield selections were able to be |
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indirectly compared to results shown in the supporting information of Tao |
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{\it et al.} \cite{Tao:2010}. Five layer thick systems, displaying a 557 facet |
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were constructed, each composed of 480 metal atoms. Double layers systems |
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were constructed from six layer thick systems where an entire layer was |
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removed from both displayed facets to create a double step. By design, the |
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double step system also contains 480 atoms, five layers thick, so energy |
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comparisons between the arrangements can be made directly. The positions |
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of the atoms were allowed to relax, along with the box sizes, before a |
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minimum energy was calculated. Carbon monoxide, equivalent to 50\% |
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coverage on one side of the metal system was added in a c(2x4) arrangement |
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and again allowed to relax before a minimum energy was calculated. |
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|
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Energies for the various systems are displayed in Table ~\ref{tab:steps}. Examining |
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the Pt systems first, it is apparent that the double layer system is slightly less stable |
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then the original single step. However, upon addition of carbon monoxide, the |
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stability is reversed and the double layer system becomes more stable. This result |
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is in agreement with DFT calculations in Tao {\it et al.}\cite{Tao:2010}, who also show |
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that the addition of CO leads to a reversal in the most stable system. While our |
359 |
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results agree qualitatively, quantitatively, they are approximately an order of magnitude |
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different. Looking at additional stability per atom in kcal/mol, the DFT calculations suggest |
361 |
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an increased stability of 0.1 kcal/mol per Pt atom, whereas we are seeing closer to a 0.4 kcal/mol |
362 |
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increase in stability per Pt atom. |
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|
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The gold systems show a much smaller energy difference between the single and double |
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systems, likely arising from their lower energy per atom values. Additionally, the weaker |
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binding of CO to Au is evidenced by the much smaller energy change between the two systems, |
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when compared to the Pt results. This limited change helps explain our lack of any reconstruction |
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on the Au systems. |
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|
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|
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%Table of single step double step calculations |
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\begin{table}[H] |
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\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.} |
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\centering |
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\begin{tabular}{| c | c | c | c | c | c | c |} |
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\hline |
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\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} \\ |
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\hline |
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Pt(557)-S & 480 & 0 & -61142.624 & -127.381 & - & 0 \\ |
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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 |
408 |
|
1200~K were performed to confirm the relative |
409 |
|
stability of the surfaces without a CO overlayer. |
410 |
|
|
411 |
< |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
412 |
< |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
413 |
< |
different temperatures for the two metals. The bare Au and Pt surfaces were |
414 |
< |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
415 |
< |
respectively for 100 ps. The two surfaces were relatively stable at these |
416 |
< |
temperatures when no CO was present, but experienced increased surface |
417 |
< |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
418 |
< |
that was initially placed in the vacuum region. Upon full adsorption, |
419 |
< |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
420 |
< |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
421 |
< |
which introduces artifacts that are not relevant to (557) reconstruction. |
422 |
< |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
423 |
< |
the Au surfaces often had a significant CO population in the gas |
424 |
< |
phase. These systems were allowed to reach thermal equilibrium (over |
425 |
< |
5~ns) before being run in the microcanonical (NVE) ensemble for |
426 |
< |
data collection. All of the systems examined had at least 40~ns in the |
427 |
< |
data collection stage, although simulation times for some Pt of the |
428 |
< |
systems exceeded 200~ns. Simulations were carried out using the open |
429 |
< |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
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 |
|
|
406 |
– |
|
407 |
– |
|
435 |
|
% RESULTS |
436 |
|
% |
437 |
|
\section{Results} |
438 |
|
\subsection{Structural remodeling} |
439 |
< |
The bare metal surfaces experienced minor roughening of the |
440 |
< |
step-edge because of the elevated temperatures, but the (557) |
441 |
< |
face was stable throughout the simulations. The surface of both |
442 |
< |
systems, upon dosage of CO, began to undergo extensive remodeling |
443 |
< |
that was not observed in the bare systems. Reconstructions of |
444 |
< |
the Au systems were limited to breakup of the step-edges and |
445 |
< |
some step wandering. The lower coverage Pt systems experienced |
446 |
< |
similar restructuring but to a greater extent. The 50\% coverage |
447 |
< |
Pt system was unique among our simulations in that it formed |
448 |
< |
well-defined and stable double layers through step coalescence, |
449 |
< |
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
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 |
|
|
424 |
– |
|
451 |
|
\subsubsection{Step wandering} |
452 |
< |
The 0\% coverage surfaces for both metals showed minimal |
453 |
< |
step-wandering at their respective temperatures. As the CO |
454 |
< |
coverage increased however, the mobility of the surface atoms, |
455 |
< |
described through adatom diffusion and step-edge wandering, |
456 |
< |
also increased. Except for the 50\% Pt system where step |
457 |
< |
coalescence occurred, the step-edges in the other simulations |
458 |
< |
preferred to keep nearly the same distance between steps as in |
459 |
< |
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
460 |
< |
Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
461 |
< |
highlights the repulsion that exists between step-edges even |
462 |
< |
when no direct interactions are present in the system. This |
463 |
< |
repulsion is caused by an entropic barrier that arises from |
464 |
< |
the fact that steps cannot cross over one another. This entropic |
465 |
< |
repulsion does not completely define the interactions between |
466 |
< |
steps, however, so it is possible to observe step coalescence |
467 |
< |
on some surfaces.\cite{Williams:1991} The presence and |
468 |
< |
concentration of adsorbates, as shown in this work, can |
469 |
< |
affect step-step interactions, potentially leading to a new |
444 |
< |
surface structure as the thermodynamic equilibrium. |
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 |
|
\subsubsection{Double layers} |
472 |
< |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
473 |
< |
undergoes two separate reconstructions upon CO adsorption. |
474 |
< |
The first involves a doubling of the step height and plateau length. |
475 |
< |
Similar behavior has been seen on a number of surfaces |
476 |
< |
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
477 |
< |
Of the two systems we examined, the Pt system showed a greater |
478 |
< |
propensity for reconstruction |
479 |
< |
because of the larger surface mobility and the greater extent of step wandering. |
480 |
< |
The amount of reconstruction was strongly correlated to the amount of CO |
481 |
< |
adsorbed upon the surface. This appears to be related to the |
482 |
< |
effect that adsorbate coverage has on edge breakup and on the |
483 |
< |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
484 |
< |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
485 |
< |
Over a longer time scale (150~ns) two more double layers formed |
486 |
< |
on this surface. Although double layer formation did not occur |
487 |
< |
in the other Pt systems, they exhibited more step-wandering and |
488 |
< |
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 layer step-edge. |
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 |
< |
The second reconstruction observed by |
494 |
< |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
495 |
< |
across the plateau between two step-edges. Neither metal, within |
496 |
< |
the 40~ns time scale or the extended simulation time of 150~ns for |
497 |
< |
the 50\% Pt system, experienced this reconstruction. |
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]{EPS_ProgressionOfDoubleLayerFormation.pdf} |
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 |
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.} |
509 |
|
\end{figure} |
510 |
|
|
511 |
|
\subsection{Dynamics} |
512 |
< |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
513 |
< |
using STM, has been able to capture the coalescence of steps |
514 |
< |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
515 |
< |
provides an upper bound for the time required for the doubling |
516 |
< |
to occur. By utilizing Molecular Dynamics we are able to probe |
517 |
< |
the dynamics of these reconstructions at elevated temperatures |
518 |
< |
and in this section we provide data on the timescales for transport |
519 |
< |
properties, e.g. diffusion and layer formation time. |
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 |
< |
The wandering of a step-edge is a cooperative effect |
525 |
< |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
526 |
< |
displaying a low index facet, (111) or (100), is unlikely to experience |
527 |
< |
much surface diffusion because of the large energetic barrier that must |
528 |
< |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
529 |
< |
on higher-index facets provides a lower energy source for mobile metal atoms. |
530 |
< |
Single-atom break-away from a step-edge on a clean surface still imposes an |
531 |
< |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
532 |
< |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
533 |
< |
The penalty lowers significantly when CO is present in sufficient quantities |
534 |
< |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
535 |
< |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
536 |
< |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
537 |
< |
able to explore the terrace before rejoining either their original step-edge or |
538 |
< |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
539 |
< |
to traverse to a separate terrace although the presence of CO can lower the |
540 |
< |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
515 |
< |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
516 |
< |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
517 |
< |
observation of the mobile metal atoms showed that they were typically in |
518 |
< |
equilibrium with the step-edges. |
519 |
< |
At times, their motion was concerted and two or more adatoms would be |
520 |
< |
observed moving together across the surfaces. |
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 |
< |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
543 |
< |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
544 |
< |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
545 |
< |
was used to prevent swamping the diffusion data with the in-place vibrational |
546 |
< |
movement of buried atoms. Diffusion on a surface is strongly affected by |
547 |
< |
local structures and in this work, the presence of single and double layer |
548 |
< |
step-edges causes the diffusion parallel to the step-edges to be larger than |
549 |
< |
the diffusion perpendicular to these edges. Parallel and perpendicular |
550 |
< |
diffusion constants are shown in Figure \ref{fig:diff}. |
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]{Portrait_DiffusionComparison_1.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 traversing along the edge as compared to |
579 |
< |
completely breaking away. The two reported diffusion constants for |
542 |
< |
the 50\% Pt system arise from different sample sets. The lower values |
543 |
< |
correspond to the same 40~ns amount that all of the other systems were |
544 |
< |
examined at, while the larger values correspond to a 20~ns period } |
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 |
|
|
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 |
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 |
|
|
562 |
– |
|
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 |
621 |
|
|
622 |
|
%Discussion |
623 |
|
\section{Discussion} |
624 |
< |
We have shown that a classical potential model is able to model the |
625 |
< |
initial reconstruction of the Pt(557) surface upon CO adsorption as |
626 |
< |
shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were |
627 |
< |
able to observe features of the dynamic processes necessary for |
628 |
< |
this reconstruction. Here we discuss the features of the model that |
629 |
< |
give rise to the observed dynamical properties of the (557) 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{Diffusion} |
633 |
< |
The perpendicular diffusion constant |
634 |
< |
appears to be the most important indicator of double layer |
635 |
< |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
636 |
< |
formation of the double layer did not begin until a nucleation |
637 |
< |
site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, |
638 |
< |
the inability for edges to cross leads to an effective edge-edge repulsion that |
639 |
< |
must be overcome to allow step coalescence. |
640 |
< |
A greater $\textbf{D}_\perp$ implies more step-wandering |
641 |
< |
and a larger chance for the stochastic meeting of two edges |
642 |
< |
to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double |
643 |
< |
layer. This helps explain why the time scale for formation after |
644 |
< |
the appearance of a nucleation site was rapid, while the initial |
645 |
< |
appearance of the nucleation site was unpredictable. |
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 |
|
\subsection{Mechanism for restructuring} |
648 |
< |
Since the Au surface showed no large scale restructuring in any of |
649 |
< |
our simulations, our discussion will focus on the 50\% Pt-CO system |
650 |
< |
which did exhibit doubling. A |
651 |
< |
number of possible mechanisms exist to explain the role of adsorbed |
652 |
< |
CO in restructuring the Pt surface. Quadrupolar repulsion between |
653 |
< |
adjacent CO molecules adsorbed on the surface is one possibility. |
654 |
< |
However, the quadrupole-quadrupole interaction is short-ranged and |
655 |
< |
is attractive for some orientations. If the CO molecules are ``locked'' in |
656 |
< |
a specific orientation relative to each other, through atop adsorption for |
657 |
< |
example, this explanation would gain credence. The calculated energetic repulsion |
658 |
< |
between two CO molecules located a distance of 2.77~\AA~apart |
659 |
< |
(nearest-neighbor distance of Pt) and both in a vertical orientation, |
660 |
< |
is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance |
661 |
< |
of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away |
662 |
< |
from a purely vertical orientation also lowers the repulsion. When the |
663 |
< |
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is |
664 |
< |
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. |
665 |
< |
The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
666 |
< |
repulsion between adjacent CO molecules bound to Pt could increase the surface |
667 |
< |
diffusion. However, the residence time of CO on Pt suggests that these |
668 |
< |
molecules are extremely mobile, with diffusion constants 40 to 2500 times |
669 |
< |
larger than surface Pt atoms. This mobility suggests that the CO molecules jump |
670 |
< |
between different Pt atoms throughout the simulation, but will stay bound for |
671 |
< |
significant periods of time. |
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 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 |
< |
A different interpretation of the above mechanism, taking into account the large |
677 |
< |
mobility of the CO, looks at how instantaneous and short-lived configurations of |
678 |
< |
CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge |
679 |
< |
breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach |
680 |
< |
an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
681 |
< |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases |
682 |
< |
(e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances, |
683 |
< |
it becomes quite energetically favorable to roughen the edge by introducing a small |
684 |
< |
separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in |
685 |
< |
simulations with significant CO populations. The roughening is present to a lesser extent |
686 |
< |
on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely |
687 |
< |
due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism |
688 |
< |
of step-edge breakup suggested by these energy curves is one of the most difficult |
689 |
< |
processes, a complete break-away from the step-edge in one unbroken movement. |
690 |
< |
Easier multistep mechanisms likely exist where an adatom moves laterally on the surface |
691 |
< |
after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest |
692 |
< |
neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher |
693 |
< |
than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO |
694 |
< |
quadrupolar repulsion is still playing a primary role, but for its importance in roughening |
695 |
< |
the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not |
696 |
< |
born out by their mobility data. The requirement for a large density of CO on the surface |
697 |
< |
for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic} |
698 |
< |
correspond well with the increased mobility seen on higher coverage surfaces. |
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=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
709 |
< |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
710 |
< |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
711 |
< |
upon them. These are a sampling of the configurations examined to gain a more |
712 |
< |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
713 |
< |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
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.pdf} |
724 |
< |
\caption{The energy curves directly correspond to the labeled model |
725 |
< |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
726 |
< |
to their initial configuration so the energy of a and h do not have the |
727 |
< |
same zero value. As is seen, certain arrangements of CO can lower |
728 |
< |
the energetic barrier that must be overcome to create an adatom. |
729 |
< |
However, it is the highest coverages where these higher-energy |
730 |
< |
configurations of CO will be more likely. } |
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 diffusion, |
735 |
< |
this does not immediately provide an explanation for the formation of double |
736 |
< |
layers. If adatoms were constrained to their terrace then doubling would be |
737 |
< |
much less likely to occur. Nucleation sites could still potentially form, but there |
738 |
< |
would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the |
739 |
< |
step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in |
692 |
< |
our simulations with our periodic treatment of the system, the system is not large enough to experience this effect. |
693 |
< |
Thus, there must be a mechanism that explains how adatoms are able to move |
694 |
< |
amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate |
695 |
< |
where an adatom along the step-edge with an adsorbed CO ``burrows'' into the |
696 |
< |
edge displacing an atom onto the higher terrace. This mechanism was chosen |
697 |
< |
because of similar events that were observed during the simulations. The barrier |
698 |
< |
heights we obtained are only approximations because we constrained the movement |
699 |
< |
of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s |
700 |
< |
are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and |
701 |
< |
this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown |
702 |
< |
in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. |
703 |
< |
While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol |
704 |
< |
difference in energies and makes the process energetically favorable. |
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]{EPS_rxnCoord.pdf} |
763 |
< |
\caption{ Various points along a reaction coordinate are displayed in the figure. |
764 |
< |
The mechanism of edge traversal is examined in the presence of CO. The approximate |
765 |
< |
barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process |
766 |
< |
is -15~kcal/mol making it an energetically favorable process.} |
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 this surface appears to require the cooperation of at least |
773 |
< |
these two described processes. For complete doubling of a layer to occur there must |
774 |
< |
be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from |
775 |
< |
that terrace they must either rise up on the ledge above them or drop to the ledge below |
776 |
< |
them. The presence of CO helps with the energetics of both of these situations. There must be sufficient |
777 |
< |
breakage of the step-edge to increase the concentration of adatoms on the surface and |
778 |
< |
these adatoms must then undergo the burrowing highlighted above or some comparable |
779 |
< |
mechanism to traverse the step-edge. Over time, these mechanisms working in concert |
780 |
< |
lead to the formation of a double layer. |
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 a double layer had formed on the 50\%~Pt system it |
786 |
< |
remained for the rest of the simulation time with minimal |
787 |
< |
movement. There were configurations that showed small |
788 |
< |
wells or peaks forming, but typically within a few nanoseconds |
789 |
< |
the feature would smooth away. Within our simulation time, |
790 |
< |
the formation of the double layer was irreversible and a double |
791 |
< |
layer was never observed to split back into two single layer |
792 |
< |
step-edges while CO was present. To further gauge the effect |
735 |
< |
CO had on this system, additional simulations were run starting |
736 |
< |
from a late configuration of the 50\%~Pt system that had formed |
737 |
< |
double layers. These simulations then had their CO removed. |
738 |
< |
The double layer breaks rapidly in these simulations, already |
739 |
< |
showing a well-defined splitting after 100~ps. Configurations of |
740 |
< |
this system are shown in Figure \ref{fig:breaking}. The coloring |
741 |
< |
of the top and bottom layers helps to exhibit how much mixing |
742 |
< |
the edges experience as they split. These systems were only |
743 |
< |
examined briefly, 10~ns, and within that time despite the initial |
744 |
< |
rapid splitting, the edges only moved another few \AA~apart. |
745 |
< |
It is possible with longer simulation times that the |
746 |
< |
(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010} |
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 |
+ |
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 |
|
|
749 |
– |
|
807 |
|
%breaking of the double layer upon removal of CO |
808 |
|
\begin{figure}[H] |
809 |
< |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking.pdf} |
810 |
< |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
811 |
< |
helped maintain the stability of the double layer and its microfaceting of the double layer |
812 |
< |
into a (111) configuration. This microfacet immediately reverts to the original (100) step |
813 |
< |
edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather |
814 |
< |
there is a mixing of the lower and upper atoms at the edge.} |
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 |
|
|
762 |
– |
|
763 |
– |
|
820 |
|
%Peaks! |
821 |
|
%\begin{figure}[H] |
822 |
|
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
830 |
|
%Don't think I need this |
831 |
|
%clean surface... |
832 |
|
%\begin{figure}[H] |
833 |
< |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
833 |
> |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF} |
834 |
|
%\caption{} |
835 |
|
|
836 |
|
%\end{figure} |
838 |
|
|
839 |
|
|
840 |
|
\section{Conclusion} |
841 |
< |
The strength of the Pt-CO binding interaction as well as the large |
842 |
< |
quadrupolar repulsion between CO molecules are sufficient to |
843 |
< |
explain the observed increase in surface mobility and the resultant |
844 |
< |
reconstructions at the highest simulated coverage. The weaker |
845 |
< |
Au-CO interaction results in lower diffusion constants, less step-wandering, |
846 |
< |
and a lack of the double layer reconstruction. An in-depth examination |
847 |
< |
of the energetics shows the important role CO plays in increasing |
848 |
< |
step-breakup and in facilitating edge traversal which are both |
793 |
< |
necessary for double layer formation. |
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 |
|
|
796 |
– |
|
854 |
|
%Things I am not ready to remove yet |
855 |
|
|
856 |
|
%Table of Diffusion Constants |
874 |
|
% \end{table} |
875 |
|
|
876 |
|
\begin{acknowledgement} |
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. |
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} |
885 |
> |
\bibstyle{achemso} |
886 |
> |
\bibliography{COonPtAu} |
887 |
|
%\end{doublespace} |
888 |
|
|
889 |
|
\begin{tocentry} |
890 |
< |
%\includegraphics[height=3.5cm]{timelapse} |
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} |