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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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%% |
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%Introduction |
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% Experimental observations |
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% Previous work on Pt, CO, etc. |
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% |
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%Simulation Methodology |
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% FF (fits and parameters) |
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% MD (setup, equilibration, collection) |
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% |
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% Analysis of trajectories!!! |
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%Discussion |
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% CO preferences for specific locales |
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% CO-CO interactions |
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% Differences between Au & Pt |
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% Causes of 2_layer reordering in Pt |
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%Summary |
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%% |
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\begin{abstract} |
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The mechanism and dynamics of surface reconstructions of Pt(557) and |
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Au(557) exposed to various coverages of carbon monoxide (CO) were |
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investigated using molecular dynamics simulations. Metal-CO |
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interactions were parameterized from experimental data and |
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plane-wave Density Functional Theory (DFT) calculations. The large |
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difference in binding strengths of the Pt-CO and Au-CO interactions |
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was found to play a significant role in step-edge stability and |
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adatom diffusion constants. Various mechanisms for CO-mediated step |
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wandering and step doubling were investigated on the Pt(557) |
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surface. We find that the energetics of CO adsorbed to the surface |
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can explain the step-doubling reconstruction observed on Pt(557) and |
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the lack of such a reconstruction on the Au(557) surface. |
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\end{abstract} |
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|
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\newpage |
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\section{Introduction} |
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% Importance: catalytically active metals are important |
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% Sub: Knowledge of how their surface structure affects their ability to catalytically facilitate certain reactions is growing, but is more reactionary than predictive |
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% Sub: Designing catalysis is the future, and will play an important role in numerous processes (ones that are currently seen to be impractical, or at least inefficient) |
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% Theory can explore temperatures and pressures which are difficult to work with in experiments |
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% Sub: Also, easier to observe what is going on and provide reasons and explanations |
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% |
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Industrial catalysts usually consist of small particles that exhibit a |
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high concentration of steps, kink sites, and vacancies at the edges of |
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the facets. These sites are thought to be the locations of catalytic |
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activity.\cite{ISI:000083038000001,ISI:000083924800001} There is now |
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significant evidence that solid surfaces are often structurally, |
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compositionally, and chemically modified by reactants under operating |
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conditions.\cite{Tao2008,Tao:2010,Tao2011} The coupling between |
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surface oxidation states and catalytic activity for CO oxidation on |
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Pt, for instance, is widely documented.\cite{Ertl08,Hendriksen:2002} |
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Despite the well-documented role of these effects on reactivity, the |
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ability to capture or predict them in atomistic models is somewhat |
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limited. While these effects are perhaps unsurprising on the highly |
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disperse, multi-faceted nanoscale particles that characterize |
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industrial catalysts, they are manifest even on ordered, well-defined |
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surfaces. The Pt(557) surface, for example, exhibits substantial and |
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reversible restructuring under exposure to moderate pressures of |
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carbon monoxide.\cite{Tao:2010} |
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|
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This work is an investigation into the mechanism and timescale for the 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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%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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molecular dynamics |
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(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
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methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
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mechanical potential energy surfaces remain out of reach. |
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Additionally, the ``bonds'' between metal atoms at a surface are |
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typically not well represented in terms of classical pairwise |
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interactions in the same way that bonds in a molecular material are, |
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nor are they captured by simple non-directional interactions like the |
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Coulomb potential. For this work, we have used classical molecular |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using 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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\subsection{Metal-metal interactions} |
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Many of the potentials used for modeling transition metals are based |
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on a non-pairwise additive functional of the local electron |
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density. The embedded atom method (EAM) is perhaps the best known of |
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these |
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methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
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but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
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the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
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parameter sets. The glue model of Ercolessi {\it et 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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\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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Here, $\rho_j(r_{ij})$ is the function that describes the distance |
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dependence of the valence electron distribution of atom $j$. The |
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contribution to the potential that comes from placing atom $i$ at that |
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location is then |
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\begin{equation*} |
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V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
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\end{equation*} |
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where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
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$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
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repulsive overlap of the two positively charged cores. |
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|
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% The {\it modified} embedded atom method (MEAM) adds angular terms to |
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% the electron density functions and an angular screening factor to the |
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% pairwise interaction between two |
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% atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve} |
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% MEAM has become widely used to simulate systems in which angular |
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% interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc |
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% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
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% MEAM presents significant additional computational costs, however. |
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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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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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\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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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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\centering |
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\begin{tabular}{| c | c | ccc |} |
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\hline |
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& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
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\hline |
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\textbf{C} & -0.6457 & 3.83 & 0.0262 & -0.75 \\ |
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\textbf{O} & 0.4843 & 3.12 & 0.1591 & -0.85 \\ |
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\textbf{M} & 0.0 & - & - & 1.6 \\ |
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\hline |
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\end{tabular} |
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\label{tab:CO} |
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\end{table} |
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\subsection{Cross-Interactions between the metals and carbon monoxide} |
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|
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Since the adsorption of CO onto a Pt surface has been the focus |
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of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
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and theoretical work |
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\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
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there is a significant amount of data on adsorption energies for CO on |
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clean metal surfaces. An earlier model by Korzeniewski {\it et |
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al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
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modified to ensure that the Pt-CO interaction favored the atop binding |
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position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
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The modified parameters yield binding energies that are slightly higher |
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than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
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{\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
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Lennard-Jones interaction to mimic strong, but short-ranged, partial |
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binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
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Pt-O interaction was modeled with a Morse potential with a large |
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equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
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over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak |
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repulsion which favors the atop site. The resulting potential-energy |
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surface suitably recovers the calculated Pt-C separation length |
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(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
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position.\cite{Deshlahra:2012, Hopster:1978} |
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|
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%where did you actually get the functionals for citation? |
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%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
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%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
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The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
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Morse potentials, respectively, to reproduce Au-CO binding energies. |
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The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
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Adsorption energies were obtained from gas-surface DFT calculations with a |
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periodic supercell plane-wave basis approach, as implemented in the |
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{\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} |
302 |
jmichalk |
3866 |
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
303 |
gezelter |
3818 |
Au x 2 Au surface planes and separated from vertical images by six |
304 |
jmichalk |
3866 |
layers of vacuum space. The surface atoms were all allowed to relax |
305 |
|
|
before CO was added to the system. Electronic relaxations were |
306 |
|
|
performed until the energy difference between subsequent steps |
307 |
|
|
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
308 |
|
|
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
309 |
gezelter |
3875 |
zone.\cite{Monkhorst:1976} The relaxed gold slab was |
310 |
gezelter |
3826 |
then used in numerous single point calculations with CO at various |
311 |
|
|
heights (and angles relative to the surface) to allow fitting of the |
312 |
|
|
empirical force field. |
313 |
gezelter |
3818 |
|
314 |
jmichalk |
3812 |
%Hint at future work |
315 |
jmichalk |
3866 |
The parameters employed for the metal-CO cross-interactions in this work |
316 |
jmichalk |
3869 |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
317 |
|
|
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
318 |
jmichalk |
3878 |
and polarization are neglected in this model, although these effects could have |
319 |
|
|
an effect on binding energies and binding site preferences. |
320 |
jmichalk |
3811 |
|
321 |
jmichalk |
3802 |
%Table of Parameters |
322 |
|
|
%Pt Parameter Set 9 |
323 |
|
|
%Au Parameter Set 35 |
324 |
|
|
\begin{table}[H] |
325 |
jmichalk |
3867 |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
326 |
jmichalk |
3869 |
interactions are modeled with Lennard-Jones potentials. While the |
327 |
jmichalk |
3867 |
metal-O interactions were fit to Morse |
328 |
gezelter |
3826 |
potentials. Distances are given in \AA~and energies in kcal/mol. } |
329 |
jmichalk |
3802 |
\centering |
330 |
|
|
\begin{tabular}{| c | cc | c | ccc |} |
331 |
|
|
\hline |
332 |
gezelter |
3826 |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\ |
333 |
jmichalk |
3802 |
\hline |
334 |
|
|
\textbf{Pt-C} & 1.3 & 15 & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\ |
335 |
|
|
\textbf{Au-C} & 1.9 & 6.5 & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\ |
336 |
|
|
|
337 |
|
|
\hline |
338 |
|
|
\end{tabular} |
339 |
jmichalk |
3866 |
\label{tab:co_parameters} |
340 |
jmichalk |
3802 |
\end{table} |
341 |
|
|
|
342 |
|
|
%Table of energies |
343 |
|
|
\begin{table}[H] |
344 |
jmichalk |
3869 |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
345 |
jmichalk |
3867 |
described in this work. All values are in eV.} |
346 |
jmichalk |
3802 |
\centering |
347 |
|
|
\begin{tabular}{| c | cc |} |
348 |
gezelter |
3826 |
\hline |
349 |
|
|
& Calculated & Experimental \\ |
350 |
|
|
\hline |
351 |
|
|
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
352 |
|
|
(Ref. \protect\cite{Kelemen:1979}) \\ |
353 |
|
|
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
354 |
gezelter |
3875 |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
355 |
gezelter |
3826 |
\hline |
356 |
jmichalk |
3802 |
\end{tabular} |
357 |
jmichalk |
3866 |
\label{tab:co_energies} |
358 |
jmichalk |
3802 |
\end{table} |
359 |
|
|
|
360 |
gezelter |
3826 |
\subsection{Pt(557) and Au(557) metal interfaces} |
361 |
jmichalk |
3872 |
Our Pt system is an orthorhombic periodic box of dimensions |
362 |
|
|
54.482~x~50.046~x~120.88~\AA~while our Au system has |
363 |
jmichalk |
3878 |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
364 |
|
|
are 9 and 8 atoms deep respectively, corresponding to a slab |
365 |
|
|
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
366 |
jmichalk |
3870 |
The systems are arranged in a FCC crystal that have been cut |
367 |
|
|
along the (557) plane so that they are periodic in the {\it x} and |
368 |
|
|
{\it y} directions, and have been oriented to expose two aligned |
369 |
|
|
(557) cuts along the extended {\it z}-axis. Simulations of the |
370 |
|
|
bare metal interfaces at temperatures ranging from 300~K to |
371 |
jmichalk |
3872 |
1200~K were performed to confirm the relative |
372 |
gezelter |
3826 |
stability of the surfaces without a CO overlayer. |
373 |
jmichalk |
3802 |
|
374 |
jmichalk |
3878 |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
375 |
jmichalk |
3876 |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
376 |
jmichalk |
3867 |
different temperatures for the two metals. The bare Au and Pt surfaces were |
377 |
gezelter |
3826 |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
378 |
jmichalk |
3869 |
respectively for 100 ps. The two surfaces were relatively stable at these |
379 |
|
|
temperatures when no CO was present, but experienced increased surface |
380 |
|
|
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
381 |
gezelter |
3826 |
that was initially placed in the vacuum region. Upon full adsorption, |
382 |
jmichalk |
3869 |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
383 |
jmichalk |
3872 |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
384 |
|
|
which introduces artifacts that are not relevant to (557) reconstruction. |
385 |
jmichalk |
3869 |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
386 |
jmichalk |
3867 |
the Au surfaces often had a significant CO population in the gas |
387 |
gezelter |
3826 |
phase. These systems were allowed to reach thermal equilibrium (over |
388 |
jmichalk |
3873 |
5~ns) before being run in the microcanonical (NVE) ensemble for |
389 |
|
|
data collection. All of the systems examined had at least 40~ns in the |
390 |
jmichalk |
3872 |
data collection stage, although simulation times for some Pt of the |
391 |
|
|
systems exceeded 200~ns. Simulations were carried out using the open |
392 |
gezelter |
3882 |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,openmd} |
393 |
jmichalk |
3802 |
|
394 |
jmichalk |
3872 |
|
395 |
|
|
|
396 |
|
|
|
397 |
|
|
% RESULTS |
398 |
|
|
% |
399 |
jmichalk |
3802 |
\section{Results} |
400 |
jmichalk |
3860 |
\subsection{Structural remodeling} |
401 |
jmichalk |
3878 |
The bare metal surfaces experienced minor roughening of the |
402 |
|
|
step-edge because of the elevated temperatures, but the (557) |
403 |
|
|
face was stable throughout the simulations. The surface of both |
404 |
|
|
systems, upon dosage of CO, began to undergo extensive remodeling |
405 |
|
|
that was not observed in the bare systems. Reconstructions of |
406 |
|
|
the Au systems were limited to breakup of the step-edges and |
407 |
|
|
some step wandering. The lower coverage Pt systems experienced |
408 |
|
|
similar restructuring but to a greater extent. The 50\% coverage |
409 |
|
|
Pt system was unique among our simulations in that it formed |
410 |
|
|
well-defined and stable double layers through step coalescence, |
411 |
|
|
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
412 |
jmichalk |
3872 |
|
413 |
|
|
|
414 |
jmichalk |
3871 |
\subsubsection{Step wandering} |
415 |
jmichalk |
3873 |
The 0\% coverage surfaces for both metals showed minimal |
416 |
jmichalk |
3878 |
step-wandering at their respective temperatures. As the CO |
417 |
|
|
coverage increased however, the mobility of the surface atoms, |
418 |
jmichalk |
3876 |
described through adatom diffusion and step-edge wandering, |
419 |
jmichalk |
3878 |
also increased. Except for the 50\% Pt system where step |
420 |
|
|
coalescence occurred, the step-edges in the other simulations |
421 |
|
|
preferred to keep nearly the same distance between steps as in |
422 |
|
|
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
423 |
|
|
Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
424 |
jmichalk |
3873 |
highlights the repulsion that exists between step-edges even |
425 |
|
|
when no direct interactions are present in the system. This |
426 |
jmichalk |
3878 |
repulsion is caused by an entropic barrier that arises from |
427 |
|
|
the fact that steps cannot cross over one another. This entropic |
428 |
|
|
repulsion does not completely define the interactions between |
429 |
|
|
steps, however, so it is possible to observe step coalescence |
430 |
|
|
on some surfaces.\cite{Williams:1991} The presence and |
431 |
|
|
concentration of adsorbates, as shown in this work, can |
432 |
|
|
affect step-step interactions, potentially leading to a new |
433 |
|
|
surface structure as the thermodynamic equilibrium. |
434 |
jmichalk |
3872 |
|
435 |
jmichalk |
3871 |
\subsubsection{Double layers} |
436 |
jmichalk |
3878 |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
437 |
|
|
undergoes two separate reconstructions upon CO adsorption. |
438 |
jmichalk |
3873 |
The first involves a doubling of the step height and plateau length. |
439 |
jmichalk |
3878 |
Similar behavior has been seen on a number of surfaces |
440 |
|
|
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
441 |
jmichalk |
3873 |
Of the two systems we examined, the Pt system showed a greater |
442 |
jmichalk |
3878 |
propensity for reconstruction |
443 |
|
|
because of the larger surface mobility and the greater extent of step wandering. |
444 |
|
|
The amount of reconstruction was strongly correlated to the amount of CO |
445 |
jmichalk |
3869 |
adsorbed upon the surface. This appears to be related to the |
446 |
jmichalk |
3873 |
effect that adsorbate coverage has on edge breakup and on the |
447 |
jmichalk |
3878 |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
448 |
|
|
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
449 |
|
|
Over a longer time scale (150~ns) two more double layers formed |
450 |
|
|
on this surface. Although double layer formation did not occur |
451 |
|
|
in the other Pt systems, they exhibited more step-wandering and |
452 |
|
|
roughening compared to their Au counterparts. The |
453 |
jmichalk |
3873 |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
454 |
jmichalk |
3876 |
various times along the simulation showing the evolution of a double layer step-edge. |
455 |
jmichalk |
3802 |
|
456 |
jmichalk |
3878 |
The second reconstruction observed by |
457 |
|
|
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
458 |
|
|
across the plateau between two step-edges. Neither metal, within |
459 |
jmichalk |
3873 |
the 40~ns time scale or the extended simulation time of 150~ns for |
460 |
|
|
the 50\% Pt system, experienced this reconstruction. |
461 |
jmichalk |
3817 |
|
462 |
jmichalk |
3876 |
%Evolution of surface |
463 |
|
|
\begin{figure}[H] |
464 |
gezelter |
3882 |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} |
465 |
jmichalk |
3876 |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
466 |
|
|
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
467 |
|
|
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
468 |
|
|
doubling of the layers appears only after two adjacent step-edges |
469 |
|
|
touch. The circled spot in (b) nucleated the growth of the double |
470 |
|
|
step observed in the later configurations.} |
471 |
|
|
\label{fig:reconstruct} |
472 |
|
|
\end{figure} |
473 |
|
|
|
474 |
jmichalk |
3860 |
\subsection{Dynamics} |
475 |
jmichalk |
3878 |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
476 |
|
|
using STM, has been able to capture the coalescence of steps |
477 |
|
|
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
478 |
|
|
provides an upper bound for the time required for the doubling |
479 |
|
|
to occur. By utilizing Molecular Dynamics we are able to probe |
480 |
|
|
the dynamics of these reconstructions at elevated temperatures |
481 |
|
|
and in this section we provide data on the timescales for transport |
482 |
|
|
properties, e.g. diffusion and layer formation time. |
483 |
gezelter |
3826 |
|
484 |
jmichalk |
3867 |
|
485 |
jmichalk |
3860 |
\subsubsection{Transport of surface metal atoms} |
486 |
jmichalk |
3862 |
%forcedSystems/stepSeparation |
487 |
jmichalk |
3878 |
The wandering of a step-edge is a cooperative effect |
488 |
jmichalk |
3873 |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
489 |
jmichalk |
3872 |
displaying a low index facet, (111) or (100), is unlikely to experience |
490 |
jmichalk |
3867 |
much surface diffusion because of the large energetic barrier that must |
491 |
jmichalk |
3873 |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
492 |
jmichalk |
3876 |
on higher-index facets provides a lower energy source for mobile metal atoms. |
493 |
jmichalk |
3878 |
Single-atom break-away from a step-edge on a clean surface still imposes an |
494 |
jmichalk |
3876 |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
495 |
jmichalk |
3870 |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
496 |
|
|
The penalty lowers significantly when CO is present in sufficient quantities |
497 |
jmichalk |
3878 |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
498 |
jmichalk |
3870 |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
499 |
jmichalk |
3878 |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
500 |
jmichalk |
3876 |
able to explore the terrace before rejoining either their original step-edge or |
501 |
jmichalk |
3878 |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
502 |
jmichalk |
3872 |
to traverse to a separate terrace although the presence of CO can lower the |
503 |
jmichalk |
3876 |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
504 |
jmichalk |
3867 |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
505 |
jmichalk |
3870 |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
506 |
jmichalk |
3867 |
observation of the mobile metal atoms showed that they were typically in |
507 |
jmichalk |
3878 |
equilibrium with the step-edges. |
508 |
jmichalk |
3870 |
At times, their motion was concerted and two or more adatoms would be |
509 |
jmichalk |
3872 |
observed moving together across the surfaces. |
510 |
gezelter |
3826 |
|
511 |
jmichalk |
3872 |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
512 |
jmichalk |
3878 |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
513 |
|
|
would typically travel much greater distances than this, but the 2~\AA~cutoff |
514 |
jmichalk |
3872 |
was used to prevent swamping the diffusion data with the in-place vibrational |
515 |
jmichalk |
3873 |
movement of buried atoms. Diffusion on a surface is strongly affected by |
516 |
jmichalk |
3870 |
local structures and in this work, the presence of single and double layer |
517 |
jmichalk |
3876 |
step-edges causes the diffusion parallel to the step-edges to be larger than |
518 |
|
|
the diffusion perpendicular to these edges. Parallel and perpendicular |
519 |
jmichalk |
3870 |
diffusion constants are shown in Figure \ref{fig:diff}. |
520 |
gezelter |
3826 |
|
521 |
jmichalk |
3876 |
%Diffusion graph |
522 |
|
|
\begin{figure}[H] |
523 |
gezelter |
3882 |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1} |
524 |
jmichalk |
3876 |
\caption{Diffusion constants for mobile surface atoms along directions |
525 |
|
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
526 |
|
|
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
527 |
|
|
surface coverage. Diffusion parallel to the step-edge is higher |
528 |
|
|
than that perpendicular to the edge because of the lower energy |
529 |
|
|
barrier associated with traversing along the edge as compared to |
530 |
|
|
completely breaking away. The two reported diffusion constants for |
531 |
|
|
the 50\% Pt system arise from different sample sets. The lower values |
532 |
|
|
correspond to the same 40~ns amount that all of the other systems were |
533 |
|
|
examined at, while the larger values correspond to a 20~ns period } |
534 |
|
|
\label{fig:diff} |
535 |
|
|
\end{figure} |
536 |
|
|
|
537 |
jmichalk |
3878 |
The weaker Au-CO interaction is evident in the weak CO-coverage |
538 |
|
|
dependance of Au diffusion. This weak interaction leads to lower |
539 |
|
|
observed coverages when compared to dosage amounts. This further |
540 |
|
|
limits the effect the CO can have on surface diffusion. The correlation |
541 |
|
|
between coverage and Pt diffusion rates shows a near linear relationship |
542 |
|
|
at the earliest times in the simulations. Following double layer formation, |
543 |
|
|
however, there is a precipitous drop in adatom diffusion. As the double |
544 |
|
|
layer forms, many atoms that had been tracked for mobility data have |
545 |
|
|
now been buried resulting in a smaller reported diffusion constant. A |
546 |
|
|
secondary effect of higher coverages is CO-CO cross interactions that |
547 |
|
|
lower the effective mobility of the Pt adatoms that are bound to each CO. |
548 |
|
|
This effect would become evident only at higher coverages. A detailed |
549 |
|
|
account of Pt adatom energetics follows in the Discussion. |
550 |
|
|
|
551 |
jmichalk |
3873 |
|
552 |
jmichalk |
3878 |
\subsubsection{Dynamics of double layer formation} |
553 |
|
|
The increased diffusion on Pt at the higher CO coverages is the primary |
554 |
|
|
contributor to double layer formation. However, this is not a complete |
555 |
|
|
explanation -- the 33\%~Pt system has higher diffusion constants, but |
556 |
|
|
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
557 |
|
|
system, one double layer formed within the first 40~ns of simulation time, |
558 |
|
|
while two more were formed as the system was allowed to run for an |
559 |
|
|
additional 110~ns (150~ns total). This suggests that this reconstruction |
560 |
|
|
is a rapid process and that the previously mentioned upper bound is a |
561 |
|
|
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
562 |
|
|
appearance of a double layer appears at 19~ns into the simulation. |
563 |
|
|
Within 12~ns of this nucleation event, nearly half of the step has formed |
564 |
|
|
the double layer and by 86~ns the complete layer has flattened out. |
565 |
|
|
From the appearance of the first nucleation event to the first observed |
566 |
|
|
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
567 |
|
|
necessary for the layer to completely straighten. The other two layers in |
568 |
|
|
this simulation formed over periods of 22~ns and 42~ns respectively. |
569 |
|
|
A possible explanation for this rapid reconstruction is the elevated |
570 |
|
|
temperatures under which our systems were simulated. The process |
571 |
|
|
would almost certainly take longer at lower temperatures. Additionally, |
572 |
|
|
our measured times for completion of the doubling after the appearance |
573 |
|
|
of a nucleation site are likely affected by our periodic boxes. A longer |
574 |
|
|
step-edge will likely take longer to ``zipper''. |
575 |
jmichalk |
3876 |
|
576 |
|
|
|
577 |
jmichalk |
3878 |
%Discussion |
578 |
|
|
\section{Discussion} |
579 |
gezelter |
3882 |
We have shown that a classical potential is able to model the initial |
580 |
|
|
reconstruction of the Pt(557) surface upon CO adsorption, and have |
581 |
|
|
reproduced the double layer structure observed by Tao {\it et |
582 |
|
|
al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be |
583 |
|
|
rapid -- occurring within 100 ns of the initial exposure to CO. Here |
584 |
|
|
we discuss the features of the classical potential that are |
585 |
|
|
contributing to the stability and speed of the Pt(557) reconstruction. |
586 |
jmichalk |
3817 |
|
587 |
jmichalk |
3878 |
\subsection{Diffusion} |
588 |
gezelter |
3882 |
The perpendicular diffusion constant appears to be the most important |
589 |
|
|
indicator of double layer formation. As highlighted in Figure |
590 |
|
|
\ref{fig:reconstruct}, the formation of the double layer did not begin |
591 |
|
|
until a nucleation site appeared. Williams {\it et |
592 |
|
|
al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge |
593 |
|
|
repulsion arising from the inability of edge crossing. This repulsion |
594 |
|
|
must be overcome to allow step coalescence. A larger |
595 |
|
|
$\textbf{D}_\perp$ value implies more step-wandering and a larger |
596 |
|
|
chance for the stochastic meeting of two edges to create a nucleation |
597 |
|
|
point. Diffusion parallel to the step-edge can help ``zipper'' up a |
598 |
|
|
nascent double layer. This helps explain the rapid time scale for |
599 |
|
|
double layer completion after the appearance of a nucleation site, while |
600 |
|
|
the initial appearance of the nucleation site was unpredictable. |
601 |
jmichalk |
3876 |
|
602 |
jmichalk |
3878 |
\subsection{Mechanism for restructuring} |
603 |
gezelter |
3882 |
Since the Au surface showed no large scale restructuring in any of our |
604 |
|
|
simulations, our discussion will focus on the 50\% Pt-CO system which |
605 |
|
|
did exhibit doubling. A number of possible mechanisms exist to explain |
606 |
|
|
the role of adsorbed CO in restructuring the Pt surface. Quadrupolar |
607 |
|
|
repulsion between adjacent CO molecules adsorbed on the surface is one |
608 |
|
|
possibility. However, the quadrupole-quadrupole interaction is |
609 |
|
|
short-ranged and is attractive for some orientations. If the CO |
610 |
|
|
molecules are ``locked'' in a vertical orientation, through atop |
611 |
|
|
adsorption for example, this explanation would gain credence. The |
612 |
|
|
calculated energetic repulsion between two CO molecules located a |
613 |
|
|
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both |
614 |
|
|
in a vertical orientation, is 8.62 kcal/mol. Moving the CO to the |
615 |
|
|
second nearest-neighbor distance of 4.8~\AA~drops the repulsion to |
616 |
|
|
nearly 0. Allowing the CO to rotate away from a purely vertical |
617 |
|
|
orientation also lowers the repulsion. When the carbons are locked at |
618 |
|
|
a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the |
619 |
|
|
angle between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
620 |
|
|
barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
621 |
|
|
repulsion between adjacent CO molecules bound to Pt could increase the |
622 |
|
|
surface diffusion. However, the residence time of CO on Pt suggests |
623 |
|
|
that the CO molecules are extremely mobile, with diffusion constants 40 |
624 |
|
|
to 2500 times larger than surface Pt atoms. This mobility suggests |
625 |
|
|
that the CO molecules jump between different Pt atoms throughout the |
626 |
|
|
simulation, but can stay bound for significant periods of time. |
627 |
jmichalk |
3876 |
|
628 |
gezelter |
3882 |
A different interpretation of the above mechanism which takes the |
629 |
|
|
large mobility of the CO into account, would be in the destabilization |
630 |
|
|
of Pt-Pt interactions due to bound CO. Destabilizing Pt-Pt bonds at |
631 |
|
|
the edges could lead to increased step-edge breakup and diffusion. On |
632 |
|
|
the bare Pt(557) surface the barrier to completely detach an edge atom |
633 |
|
|
is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
634 |
|
|
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain |
635 |
|
|
configurations, cases (e), (g), and (h), the barrier can be lowered to |
636 |
|
|
$\sim$23~kcal/mol by the presence of bound CO molecules. In these |
637 |
|
|
instances, it becomes energetically favorable to roughen the edge by |
638 |
|
|
introducing a small separation of 0.5 to 1.0~\AA. This roughening |
639 |
|
|
becomes immediately obvious in simulations with significant CO |
640 |
|
|
populations. The roughening is present to a lesser extent on surfaces |
641 |
|
|
with lower CO coverage (and even on the bare surfaces), although in |
642 |
|
|
these cases it is likely due to random fluctuations that squeeze out |
643 |
|
|
step-edge atoms. Step-edge breakup by continuous single-atom |
644 |
|
|
translations (as suggested by these energy curves) is probably a |
645 |
|
|
worst-case scenario. Multistep mechanisms in which an adatom moves |
646 |
|
|
laterally on the surface after being ejected would be more |
647 |
|
|
energetically favorable. This would leave the adatom alongside the |
648 |
|
|
ledge, providing it with 5 nearest neighbors. While fewer than the 7 |
649 |
|
|
neighbors it had as part of the step-edge, it keeps more Pt neighbors |
650 |
|
|
than the 3 an isolated adatom would have on the terrace. In this |
651 |
|
|
proposed mechanism, the CO quadrupolar repulsion still plays a role in |
652 |
|
|
the initial roughening of the step-edge, but not in any long-term |
653 |
|
|
bonds with individual Pt atoms. Higher CO coverages create more |
654 |
|
|
opportunities for the crowded CO configurations shown in Figure |
655 |
|
|
\ref{fig:SketchGraphic}, and this is likely to cause an increased |
656 |
|
|
propensity for step-edge breakup. |
657 |
jmichalk |
3876 |
|
658 |
|
|
%Sketch graphic of different configurations |
659 |
jmichalk |
3816 |
\begin{figure}[H] |
660 |
gezelter |
3882 |
\includegraphics[width=\linewidth]{COpaths} |
661 |
|
|
\caption{Configurations used to investigate the mechanism of step-edge |
662 |
|
|
breakup on Pt(557). In each case, the central (starred) atom is |
663 |
|
|
pulled directly across the surface away from the step edge. The Pt |
664 |
|
|
atoms on the upper terrace are colored dark grey, while those on the |
665 |
|
|
lower terrace are in white. In each of these configurations, some |
666 |
|
|
number of the atoms (highlighted in blue) had a CO molecule bound in |
667 |
|
|
a vertical atop position. The energies of these configurations as a |
668 |
|
|
function of central atom displacement are displayed in Figure |
669 |
|
|
\ref{fig:SketchEnergies}.} |
670 |
jmichalk |
3876 |
\label{fig:SketchGraphic} |
671 |
jmichalk |
3862 |
\end{figure} |
672 |
|
|
|
673 |
jmichalk |
3876 |
%energy graph corresponding to sketch graphic |
674 |
jmichalk |
3862 |
\begin{figure}[H] |
675 |
gezelter |
3882 |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison} |
676 |
|
|
\caption{Energies for displacing a single edge atom perpendicular to |
677 |
|
|
the step edge as a function of atomic displacement. Each of the |
678 |
|
|
energy curves corresponds to one of the labeled configurations in |
679 |
|
|
Figure \ref{fig:SketchGraphic}, and are referenced to the |
680 |
|
|
unperturbed step-edge. Certain arrangements of bound CO (notably |
681 |
|
|
configurations g and h) can lower the energetic barrier for creating |
682 |
|
|
an adatom relative to the bare surface (configuration a).} |
683 |
jmichalk |
3876 |
\label{fig:SketchEnergies} |
684 |
jmichalk |
3816 |
\end{figure} |
685 |
|
|
|
686 |
gezelter |
3882 |
While configurations of CO on the surface are able to increase |
687 |
|
|
diffusion and the likelihood of edge wandering, this does not provide |
688 |
|
|
a complete explanation for the formation of double layers. If adatoms |
689 |
|
|
were constrained to their original terraces then doubling could not |
690 |
|
|
occur. A mechanism for vertical displacement of adatoms at the |
691 |
|
|
step-edge is required to explain the doubling. |
692 |
jmichalk |
3802 |
|
693 |
gezelter |
3882 |
We have discovered one possible mechanism for a CO-mediated vertical |
694 |
|
|
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} |
695 |
|
|
shows four points along a reaction coordinate in which a CO-bound |
696 |
|
|
adatom along the step-edge ``burrows'' into the edge and displaces the |
697 |
|
|
original edge atom onto the higher terrace. A number of events similar |
698 |
|
|
to this mechanism were observed during the simulations. We predict an |
699 |
|
|
energetic barrier of 20~kcal/mol for this process (in which the |
700 |
|
|
displaced edge atom follows a curvilinear path into an adjacent 3-fold |
701 |
|
|
hollow site). The barrier heights we obtain for this reaction |
702 |
|
|
coordinate are approximate because the exact path is unknown, but the |
703 |
|
|
calculated energy barriers would be easily accessible at operating |
704 |
|
|
conditions. Additionally, this mechanism is exothermic, with a final |
705 |
|
|
energy 15~kcal/mol below the original $\lambda = 0$ configuration. |
706 |
|
|
When CO is not present and this reaction coordinate is followed, the |
707 |
|
|
process is endothermic by 3~kcal/mol. The difference in the relative |
708 |
|
|
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present |
709 |
|
|
provides strong support for CO-mediated Pt-Pt interactions giving rise |
710 |
|
|
to the doubling reconstruction. |
711 |
|
|
|
712 |
jmichalk |
3862 |
%lambda progression of Pt -> shoving its way into the step |
713 |
|
|
\begin{figure}[H] |
714 |
gezelter |
3882 |
\includegraphics[width=\linewidth]{EPS_rxnCoord} |
715 |
|
|
\caption{Points along a possible reaction coordinate for CO-mediated |
716 |
|
|
edge doubling. Here, a CO-bound adatom burrows into an established |
717 |
|
|
step edge and displaces an edge atom onto the upper terrace along a |
718 |
|
|
curvilinear path. The approximate barrier for the process is |
719 |
|
|
20~kcal/mol, and the complete process is exothermic by 15~kcal/mol |
720 |
|
|
in the presence of CO, but is endothermic by 3~kcal/mol without.} |
721 |
jmichalk |
3862 |
\label{fig:lambda} |
722 |
|
|
\end{figure} |
723 |
|
|
|
724 |
gezelter |
3882 |
The mechanism for doubling on the Pt(557) surface appears to require |
725 |
|
|
the cooperation of at least two distinct processes. For complete |
726 |
|
|
doubling of a layer to occur there must be a breakup of one |
727 |
|
|
terrace. These atoms must then ``disappear'' from that terrace, either |
728 |
|
|
by travelling to the terraces above of below their original levels. |
729 |
|
|
The presence of CO helps explain mechanisms for both of these |
730 |
|
|
situations. There must be sufficient breakage of the step-edge to |
731 |
|
|
increase the concentration of adatoms on the surface and these adatoms |
732 |
|
|
must then undergo the burrowing highlighted above (or a comparable |
733 |
|
|
mechanism) to create the double layer. With sufficient time, these |
734 |
|
|
mechanisms working in concert lead to the formation of a double layer. |
735 |
jmichalk |
3879 |
|
736 |
jmichalk |
3878 |
\subsection{CO Removal and double layer stability} |
737 |
gezelter |
3882 |
Once a double layer had formed on the 50\%~Pt system, it remained for |
738 |
|
|
the rest of the simulation time with minimal movement. Random |
739 |
|
|
fluctuations that involved small clusters or divots were observed, but |
740 |
|
|
these features typically healed within a few nanoseconds. Within our |
741 |
|
|
simulations, the formation of the double layer appeared to be |
742 |
|
|
irreversible and a double layer was never observed to split back into |
743 |
|
|
two single layer step-edges while CO was present. |
744 |
jmichalk |
3862 |
|
745 |
gezelter |
3882 |
To further gauge the effect CO has on this surface, additional |
746 |
|
|
simulations were run starting from a late configuration of the 50\%~Pt |
747 |
|
|
system that had already formed double layers. These simulations then |
748 |
|
|
had their CO forcibly removed. The double layer broke apart rapidly |
749 |
|
|
in these simulations, showing a well-defined edge-splitting after |
750 |
|
|
100~ps. Configurations of this system are shown in Figure |
751 |
|
|
\ref{fig:breaking}. The coloring of the top and bottom layers helps to |
752 |
|
|
exhibit how much mixing the edges experience as they split. These |
753 |
|
|
systems were only examined for 10~ns, and within that time despite the |
754 |
|
|
initial rapid splitting, the edges only moved another few |
755 |
|
|
\AA~apart. It is possible that with longer simulation times, the (557) |
756 |
|
|
surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could |
757 |
|
|
also be recovered. |
758 |
jmichalk |
3862 |
|
759 |
|
|
%breaking of the double layer upon removal of CO |
760 |
jmichalk |
3802 |
\begin{figure}[H] |
761 |
gezelter |
3882 |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} |
762 |
|
|
\caption{Dynamics of an established (111) double step after removal of |
763 |
|
|
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal |
764 |
|
|
of CO. The presence of the CO helped maintain the stability of the |
765 |
|
|
double step. Nearly immediately after the CO is removed, the step |
766 |
|
|
edge reforms in a (100) configuration, which is also the step type |
767 |
|
|
seen on clean (557) surfaces. The step separation involves |
768 |
|
|
significant mixing of the lower and upper atoms at the edge.} |
769 |
jmichalk |
3862 |
\label{fig:breaking} |
770 |
jmichalk |
3802 |
\end{figure} |
771 |
|
|
|
772 |
|
|
|
773 |
|
|
%Peaks! |
774 |
jmichalk |
3872 |
%\begin{figure}[H] |
775 |
|
|
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
776 |
|
|
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
777 |
|
|
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
778 |
|
|
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
779 |
|
|
%\label{fig:peaks} |
780 |
|
|
%\end{figure} |
781 |
jmichalk |
3862 |
|
782 |
jmichalk |
3867 |
|
783 |
|
|
%Don't think I need this |
784 |
jmichalk |
3862 |
%clean surface... |
785 |
jmichalk |
3867 |
%\begin{figure}[H] |
786 |
gezelter |
3882 |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF} |
787 |
jmichalk |
3867 |
%\caption{} |
788 |
jmichalk |
3862 |
|
789 |
jmichalk |
3867 |
%\end{figure} |
790 |
|
|
%\label{fig:clean} |
791 |
|
|
|
792 |
|
|
|
793 |
jmichalk |
3802 |
\section{Conclusion} |
794 |
gezelter |
3882 |
The strength and directionality of the Pt-CO binding interaction, as |
795 |
|
|
well as the large quadrupolar repulsion between atop-bound CO |
796 |
|
|
molecules, help to explain the observed increase in surface mobility |
797 |
|
|
of Pt(557) and the resultant reconstruction into a double-layer |
798 |
|
|
configuration at the highest simulated CO-coverages. The weaker Au-CO |
799 |
|
|
interaction results in significantly lower adataom diffusion |
800 |
|
|
constants, less step-wandering, and a lack of the double layer |
801 |
|
|
reconstruction on the Au(557) surface. |
802 |
jmichalk |
3802 |
|
803 |
gezelter |
3882 |
An in-depth examination of the energetics shows the important role CO |
804 |
|
|
plays in increasing step-breakup and in facilitating edge traversal |
805 |
|
|
which are both necessary for double layer formation. |
806 |
jmichalk |
3880 |
|
807 |
jmichalk |
3862 |
%Things I am not ready to remove yet |
808 |
|
|
|
809 |
|
|
%Table of Diffusion Constants |
810 |
|
|
%Add gold?M |
811 |
|
|
% \begin{table}[H] |
812 |
|
|
% \caption{} |
813 |
|
|
% \centering |
814 |
|
|
% \begin{tabular}{| c | cc | cc | } |
815 |
|
|
% \hline |
816 |
|
|
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
817 |
|
|
% \hline |
818 |
|
|
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
819 |
|
|
% \hline |
820 |
|
|
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
821 |
|
|
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
822 |
|
|
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
823 |
|
|
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
824 |
|
|
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
825 |
|
|
% \hline |
826 |
|
|
% \end{tabular} |
827 |
|
|
% \end{table} |
828 |
|
|
|
829 |
gezelter |
3875 |
\begin{acknowledgement} |
830 |
gezelter |
3882 |
We gratefully acknowledge conversations with Dr. William |
831 |
|
|
F. Schneider and Dr. Feng Tao. Support for this project was |
832 |
|
|
provided by the National Science Foundation under grant CHE-0848243 |
833 |
|
|
and by the Center for Sustainable Energy at Notre Dame |
834 |
|
|
(cSEND). Computational time was provided by the Center for Research |
835 |
|
|
Computing (CRC) at the University of Notre Dame. |
836 |
gezelter |
3875 |
\end{acknowledgement} |
837 |
gezelter |
3808 |
\newpage |
838 |
|
|
\bibliography{firstTryBibliography} |
839 |
gezelter |
3875 |
%\end{doublespace} |
840 |
|
|
|
841 |
|
|
\begin{tocentry} |
842 |
|
|
%\includegraphics[height=3.5cm]{timelapse} |
843 |
jmichalk |
3884 |
\includegraphics[height=3.5cm]{TOC_doubleLayer.pdf} |
844 |
gezelter |
3875 |
\end{tocentry} |
845 |
|
|
|
846 |
gezelter |
3808 |
\end{document} |