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\begin{document} |
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%% |
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%Introduction |
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% Experimental observations |
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% 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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%Title |
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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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\author{Joseph R. Michalka, Patrick W. McIntyre and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
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Department of Chemistry and Biochemistry,\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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%Date |
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\date{Dec 15, 2012} |
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%authors |
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|
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% make the title |
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\maketitle |
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|
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\begin{doublespace} |
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|
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\begin{abstract} |
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|
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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 an effort to understand the mechanism and timescale for |
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surface restructuring using molecular simulations. Since the dynamics |
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of the process is of particular interest, we utilize classical force |
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fields that represent a compromise between chemical accuracy and the |
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computational efficiency necessary to observe the process of interest. |
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|
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Since restructuring occurs as a result of specific interactions of the |
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catalyst with adsorbates, two metal systems exposed to carbon monoxide |
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were examined in this work. The Pt(557) surface has already been shown |
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to reconstruct under certain conditions. The Au(557) surface, because |
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of a weaker interaction with CO, is less likely to undergo this kind |
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of reconstruction. MORE HERE ON PT AND AU PREVIOUS WORK. |
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|
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%Platinum molecular dynamics |
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%gold molecular dynamics |
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\section{Simulation Methods} |
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The challenge in modeling any solid/gas interface problem is the |
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development of a sufficiently general yet computationally tractable |
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model of the chemical interactions between the surface atoms and |
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adsorbates. Since the interfaces involved are quite large (10$^3$ - |
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10$^6$ atoms) and respond slowly to perturbations, {\it ab initio} |
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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, while modeling the CO using a rigid |
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three-site model developed by Straub and Karplus for studying |
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photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
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Pt-CO cross interactions were parameterized as part of this work. |
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|
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\subsection{Metal-metal interactions} |
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Many of the potentials used for modeling transition metals are based |
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on a non-pairwise additive functional of the local electron |
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density. The embedded atom method (EAM) is perhaps the best known of |
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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.} is among the |
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fastest of these density functional approaches.\cite{Ercolessi88} In |
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all of these models, atoms are conceptualized as a positively charged |
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core with a radially-decaying valence electron distribution. To |
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calculate the energy for embedding the core at a particular location, |
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the electron density due to the valence electrons at all of the other |
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atomic sites is computed at atom $i$'s location, |
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\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 an pairwise term that is meant to represent the |
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overlap of the two positively charged cores. |
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|
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% The {\it modified} embedded atom method (MEAM) adds angular terms to |
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% the electron density functions and an angular screening factor to the |
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% pairwise interaction between two |
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% atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve} |
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% MEAM has become widely used to simulate systems in which angular |
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% interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc |
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% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
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% MEAM presents significant additional computational costs, however. |
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|
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The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen 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} All of these potentials have their |
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strengths and weaknesses. One of the strengths common to all of the |
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methods is the relatively large library of metals for which these |
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potentials have been |
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parameterized.\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
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|
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\subsection{Carbon Monoxide model} |
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Since previous explanations for the surface rearrangements center on |
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the large linear quadrupole moment of carbon monoxide, the model |
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chosen for this molecule exhibits this property in an efficient |
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manner. We used a model first proposed by Karplus and Straub to study |
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the photodissociation of CO from myoglobin.\cite{Straub} The Straub and |
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Karplus model is a rigid three site model which places a massless M |
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site at the center of mass along the CO bond. The geometry used along |
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with the interaction parameters are reproduced in Table~1. The effective |
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dipole moment, calculated from the assigned charges, is still |
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small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
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to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
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mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
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%CO Table |
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\begin{table}[H] |
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\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
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$\epsilon$), and charges for the CO-CO |
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interactions borrowed from Ref. \bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA~, energies are |
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in kcal/mol, and charges are in atomic units.} |
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\centering |
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\begin{tabular}{| c | c | ccc |} |
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\hline |
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& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
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\hline |
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\textbf{C} & -0.6457 & 0.0262 & 3.83 & -0.75 \\ |
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\textbf{O} & 0.4843 & 0.1591 & 3.12 & -0.85 \\ |
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\textbf{M} & 0.0 & - & - & 1.6 \\ |
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\hline |
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\end{tabular} |
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\end{table} |
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\subsection{Cross-Interactions between the metals and carbon monoxide} |
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Since the adsorption of CO onto a platinum surface has been the focus |
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of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
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and theoretical work |
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\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
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there is a significant amount of data on adsorption energies for CO on |
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clean metal surfaces. Parameters reported by Korzeniewski {\it et |
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al.}\cite{Pons:1986} were a starting point for our fits, which were |
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modified to ensure that the Pt-CO interaction favored the atop binding |
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position on Pt(111). This resulting binding energies are on the higher |
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side of the experimentally-reported values. Following Korzeniewski |
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{\it et al.},\cite{Pons:1986} the Pt-C interaction was fit to a deep |
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Lennard-Jones interaction to mimic strong, but short-ranged partial |
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binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
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Pt-O interaction was parameterized to a Morse potential with a large |
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range parameter ($r_o$). In most cases, this contributes a weak |
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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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%where did you actually get the functionals for citation? |
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%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
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%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
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The Au-C and Au-O cross-interactions were fit using Lennard-Jones and |
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Morse potentials, respectively, to reproduce Au-CO binding energies. |
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The fits were refined against gas-surface DFT calculations with a |
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periodic supercell plane-wave basis approach, as implemented in the |
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{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores are |
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described with the projector augmented-wave (PAW) |
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method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
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included to an energy cutoff of 20 Ry. Electronic energies are |
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computed with the PBE implementation of the generalized gradient |
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approximation (GGA) for gold, carbon, and oxygen that was constructed |
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by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
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Ionic relaxations were performed until the energy difference between |
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subsequent steps was less than $10^{-8}$ Ry. In testing the CO-Au |
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interaction, Au(111) supercells were constructed of four layers of 4 |
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Au x 2 Au surface planes and separated from vertical images by six |
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layers of vacuum space. The surface atoms were all allowed to relax. |
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Supercell calculations were performed nonspin-polarized with a 4 x 4 x |
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4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
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zone.\cite{Monkhorst:1976,PhysRevB.13.5188} The relaxed gold slab was |
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then used in numerous single point calculations with CO at various |
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heights (and angles relative to the surface) to allow fitting of the |
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empirical force field. |
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|
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%Hint at future work |
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The parameters employed in this work are shown in Table 2 and the |
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binding energies on the 111 surfaces are displayed in Table 3. To |
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speed up the computations, charge transfer and polarization are not |
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being treated in this model, although these effects are likely to |
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affect binding energies and binding site |
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preferences.\cite{Deshlahra:2012} |
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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 potential, while the |
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(mostly-repulsive) metal-O interactions were fit to Morse |
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potentials. Distances are given in \AA~and energies in kcal/mol. } |
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\centering |
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\begin{tabular}{| c | cc | c | ccc |} |
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\hline |
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& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\ |
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\hline |
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\textbf{Pt-C} & 1.3 & 15 & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\ |
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\textbf{Au-C} & 1.9 & 6.5 & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\ |
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\hline |
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\end{tabular} |
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\end{table} |
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%Table of energies |
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\begin{table}[H] |
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\caption{Adsorption energies for CO on M(111) using the potentials |
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described in this work. All values are in eV} |
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\centering |
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\begin{tabular}{| c | cc |} |
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\hline |
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& Calculated & Experimental \\ |
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\hline |
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\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
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(Ref. \protect\cite{Kelemen:1979}) \\ |
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& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
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\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPD_Gold}) \\ |
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\hline |
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\end{tabular} |
315 |
|
|
\end{table} |
316 |
|
|
|
317 |
gezelter |
3826 |
\subsection{Pt(557) and Au(557) metal interfaces} |
318 |
jmichalk |
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|
319 |
jmichalk |
3827 |
Our model systems are composed of 3888 Pt atoms and 3384 Au atoms in a |
320 |
gezelter |
3826 |
FCC crystal that have been cut along the 557 plane so that they are |
321 |
|
|
periodic in the {\it x} and {\it y} directions, and have been rotated |
322 |
|
|
to expose two parallel 557 cuts along the positive and negative {\it |
323 |
|
|
z}-axis. Simulations of the bare metal interfaces at temperatures |
324 |
|
|
ranging from 300~K to 1200~K were done to observe the relative |
325 |
|
|
stability of the surfaces without a CO overlayer. |
326 |
jmichalk |
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|
327 |
gezelter |
3826 |
The different bulk (and surface) melting temperatures (1337~K for Au |
328 |
|
|
and 2045~K for Pt) suggest that the reconstruction may happen at |
329 |
|
|
different temperatures for the two metals. To copy experimental |
330 |
|
|
conditions for the CO-exposed surfaces, the bare surfaces were |
331 |
|
|
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
332 |
|
|
respectively for 100 ps. Each surface was exposed to a range of CO |
333 |
|
|
that was initially placed in the vacuum region. Upon full adsorption, |
334 |
|
|
these amounts correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
335 |
|
|
coverage. Because of the difference in binding energies, the platinum |
336 |
|
|
systems very rarely had CO that was not bound to the surface, while |
337 |
|
|
the gold surfaces often had a significant CO population in the gas |
338 |
|
|
phase. These systems were allowed to reach thermal equilibrium (over |
339 |
|
|
5 ns) before being shifted to the microcanonical (NVE) ensemble for |
340 |
|
|
data collection. All of the systems examined had at least 40 ns in the |
341 |
|
|
data collection stage, although simulation times for some of the |
342 |
|
|
systems exceeded 200ns. All simulations were run using the open |
343 |
|
|
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,OpenMD} |
344 |
jmichalk |
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|
345 |
|
|
% Just results, leave discussion for discussion section |
346 |
jmichalk |
3860 |
% structure |
347 |
|
|
% Pt: step wandering, double layers, no triangular motifs |
348 |
|
|
% Au: step wandering, no double layers |
349 |
|
|
% dynamics |
350 |
|
|
% diffusion |
351 |
|
|
% time scale, formation, breakage |
352 |
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\section{Results} |
353 |
jmichalk |
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\subsection{Structural remodeling} |
354 |
|
|
Tao {\it et al.} showed experimentally that the Pt(557) surface undergoes |
355 |
|
|
two separate reconstructions upon CO adsorption.\cite{Tao:2010} The first |
356 |
|
|
reconstruction involves a doubling of the step height and plateau length. Similar |
357 |
jmichalk |
3862 |
behavior has been seen to occur on numerous surfaces at varying conditions.\cite{Williams:1994,Williams:1991,Pearl} |
358 |
jmichalk |
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Of the two systems we examined, the Platinum system showed the most surface |
359 |
|
|
reconstruction. Additionally, the amount of reconstruction appears to be |
360 |
|
|
dependent on the amount of CO adsorbed upon the surface. This result is likely |
361 |
|
|
related to the effect that coverage has on surface diffusion. While both systems |
362 |
|
|
displayed step edge wandering, only the Pt surface underwent doubling within |
363 |
|
|
the time scales we were modeling. Specifically only the 50 \% coverage Pt system |
364 |
jmichalk |
3862 |
was observed to undergo a complete doubling in the time scales we were able to monitor. |
365 |
|
|
This event encouraged us to allow that specific system to run continuously during which two |
366 |
|
|
more double layers were created. The other systems, not displaying any large scale changes |
367 |
|
|
of interest, were all stopped after 40 ns of simulation. Neverthless, the other Platinum systems tended to show |
368 |
|
|
more cumulative lateral movement of the step edges when compared to the Gold systems. |
369 |
|
|
The 50 \% Pt system is highlighted in figure \ref{fig:reconstruct} at various times along the |
370 |
|
|
simulation showing the evolution of the system. |
371 |
jmichalk |
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|
372 |
jmichalk |
3860 |
The second reconstruction on the Pt(557) surface observed by Tao involved the |
373 |
|
|
formation of triangular clusters that stretched across the plateau between two step edges. |
374 |
|
|
Neither system, within our simulated time scales, experiences this reconstruction. A constructed |
375 |
|
|
system in which the triangular motifs were constructed on the surface will be explored in future |
376 |
|
|
work and is shown in the supporting information. |
377 |
jmichalk |
3817 |
|
378 |
jmichalk |
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\subsection{Dynamics} |
379 |
jmichalk |
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While atomistic-like simulations of stepped surfaces have been performed before \cite{}, they tend to be |
380 |
|
|
performed using Monte Carlo techniques\cite{Williams:1991,Williams:1994}. This allows them to efficiently sample the thermodynamic |
381 |
|
|
landscape but at the expense of ignoring the dynamics of the system. Previous work, using STM \cite{Pearl}, |
382 |
|
|
has been able to visualize the coalescing of steps of (system). The time scale of the image acquisition, ~ 70 s/image |
383 |
jmichalk |
3860 |
provides an upper bounds for the time required for the doubling to actually occur. While statistical treatments |
384 |
|
|
of step edges are adept at analyzing such systems, it is important to remember that the edges are made |
385 |
|
|
up of individual atoms and thus can be examined in numerous ways. |
386 |
gezelter |
3826 |
|
387 |
jmichalk |
3860 |
\subsubsection{Transport of surface metal atoms} |
388 |
jmichalk |
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%forcedSystems/stepSeparation |
389 |
jmichalk |
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The movement of a step edge is a cooperative effect arising from the individual movements of the atoms |
390 |
|
|
making up the step. An ideal metal surface displaying a low index facet (111, 100, 110) is unlikely to |
391 |
|
|
experience much surface diffusion because of the large energetic barrier to lift an atom out of the surface. |
392 |
jmichalk |
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For our surfaces however, the presence of step edges provide a source for mobile metal atoms. Breaking away |
393 |
|
|
from the step edge still imposes an energetic penalty around 40 kcal/mole, but is much less than lifting the same metal |
394 |
|
|
atom out from the surface, > 60 kcal/mole, and the penalty lowers even further when CO is present in sufficient quantities |
395 |
|
|
on the surface, ~20 kcal/mole. Once an adatom exists on the surface, its barrier for diffusion is negligible ( < 4 kcal/mole) |
396 |
|
|
and is well able to explore its terrace. Atoms traversing terraces is more difficult, but can be overcome through a joining and lifting stage. |
397 |
|
|
By tracking the mobility of individual metal atoms on the Platinum and Gold surfaces we were able to determine |
398 |
|
|
the relative diffusion rates and how varying coverages of CO affected the rates. Close |
399 |
jmichalk |
3860 |
observation of the mobile metal atoms showed that they were typically in equilibrium with the |
400 |
|
|
step edges, constantly breaking apart and rejoining. Additionally, at times their motion was concerted and |
401 |
|
|
two or more atoms would be observed moving together across the surfaces. The primary challenge in quantifying |
402 |
jmichalk |
3862 |
the overall surface mobility was in defining ``mobile" vs. ``static" atoms. |
403 |
gezelter |
3826 |
|
404 |
jmichalk |
3860 |
A particle was considered mobile once it had traveled more than 2~\AA~ between saved configurations |
405 |
|
|
of the system (10-100 ps). An atom that was truly mobile would typically travel much greater than this, but |
406 |
jmichalk |
3862 |
the 2~\AA~ cutoff was to prevent the in-place vibrational movement of atoms from being included in the analysis. |
407 |
jmichalk |
3860 |
Since diffusion on a surface is strongly affected by local structures, in this case the presence of single and double |
408 |
|
|
layer step edges, the diffusion parallel to the step edges was determined separately from the diffusion perpendicular |
409 |
|
|
to these edges. The parallel and perpendicular diffusion constants are shown in figure \ref{fig:diff}. |
410 |
gezelter |
3826 |
|
411 |
jmichalk |
3860 |
\subsubsection{Double layer formation} |
412 |
|
|
The increased amounts of diffusion on Pt at the higher CO coverages appears to play a role in the |
413 |
jmichalk |
3862 |
formation of double layers, seeing as how that was the only system within our observed simulation time |
414 |
|
|
that showed the formation. Despite this being the only system where this reconstruction occurs, three separate layers |
415 |
|
|
were formed over the extended run time of this system. As mentioned earlier, previous experimental work has given some insight into |
416 |
|
|
the upper bounds of the time required for enough atoms to move around to allow two steps to coalesce\cite{Williams:1991,Pearl}. |
417 |
jmichalk |
3860 |
As seen in figure \ref{fig:reconstruct}, the first appearance of a double layer, a nodal site, appears at 19 ns into |
418 |
jmichalk |
3862 |
the simulation. Within 12 ns, nearly half of the step has formed the double layer and by 86 ns, a smooth complete |
419 |
|
|
layer has formed. The double layer is complete by 37 ns but is a bit rough. |
420 |
|
|
From the appearance of the first node to the initial doubling of the layers ignoring their roughness took ~20 ns. |
421 |
|
|
Another ~40 ns was necessary for the layer to completely straighten. The other two layers in this simulation form |
422 |
|
|
over a period of 22 ns and 42 ns respectively. |
423 |
jmichalk |
3817 |
|
424 |
jmichalk |
3862 |
%Evolution of surface |
425 |
jmichalk |
3816 |
\begin{figure}[H] |
426 |
jmichalk |
3862 |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
427 |
|
|
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
428 |
|
|
initial exposure to the CO: (a) 258 ps, (b) 19 ns, (c) 31.2 ns, and |
429 |
|
|
(d) 86.1 ns. Disruption of the 557 step edges occurs quickly. The |
430 |
|
|
doubling of the layers appears only after two adjacent step edges |
431 |
|
|
touch. The circled spot in (b) nucleated the growth of the double |
432 |
|
|
step observed in the later configurations.} |
433 |
|
|
\label{fig:reconstruct} |
434 |
|
|
\end{figure} |
435 |
|
|
|
436 |
|
|
\begin{figure}[H] |
437 |
jmichalk |
3839 |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade.pdf} |
438 |
gezelter |
3826 |
\caption{Diffusion constants for mobile surface atoms along directions |
439 |
|
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
440 |
|
|
($\mathbf{D}_{\perp}$) to the 557 step edges as a function of CO |
441 |
|
|
surface coverage. Diffusion parallel to the step edge is higher |
442 |
|
|
than that perpendicular to the edge because of the lower energy |
443 |
|
|
barrier associated with going from approximately 7 nearest neighbors |
444 |
|
|
to 5, as compared to the 3 of an adatom. Additionally, the observed |
445 |
|
|
maximum and subsequent decrease for the Pt system suggests that the |
446 |
|
|
CO self-interactions are playing a significant role with regards to |
447 |
|
|
movement of the platinum atoms around and more importantly across |
448 |
|
|
the surface. } |
449 |
|
|
\label{fig:diff} |
450 |
jmichalk |
3816 |
\end{figure} |
451 |
|
|
|
452 |
jmichalk |
3802 |
|
453 |
jmichalk |
3862 |
|
454 |
|
|
|
455 |
jmichalk |
3802 |
%Discussion |
456 |
|
|
\section{Discussion} |
457 |
jmichalk |
3862 |
In this paper we have shown that we were able to accurately model the initial reconstruction of the |
458 |
|
|
Pt (557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
459 |
|
|
were able to capture the dynamic processes inherent within this reconstruction. |
460 |
jmichalk |
3802 |
|
461 |
jmichalk |
3862 |
\subsection{Mechanism for restructuring} |
462 |
|
|
The increased computational cost to examine this system using molecular dynamics rather than |
463 |
|
|
a Monte Carlo based approach was necessary so that our predictions on possible mechanisms |
464 |
|
|
and driving forces would have support not only from thermodynamic arguments but also from the |
465 |
|
|
actual dynamics of the system. |
466 |
gezelter |
3826 |
|
467 |
|
|
Comparing the results from simulation to those reported previously by |
468 |
|
|
Tao et al. the similarities in the platinum and CO system are quite |
469 |
jmichalk |
3862 |
strong. As shown in figure \ref{fig:reconstruct}, the simulated platinum system under a CO |
470 |
gezelter |
3826 |
atmosphere will restructure slightly by doubling the terrace |
471 |
|
|
heights. The restructuring appears to occur slowly, one to two |
472 |
|
|
platinum atoms at a time. Looking at individual snapshots, these |
473 |
|
|
adatoms tend to either rise on top of the plateau or break away from |
474 |
|
|
the step edge and then diffuse perpendicularly to the step direction |
475 |
|
|
until reaching another step edge. This combination of growth and decay |
476 |
|
|
of the step edges appears to be in somewhat of a state of dynamic |
477 |
|
|
equilibrium. However, once two previously separated edges meet as |
478 |
|
|
shown in figure 1.B, this point tends to act as a focus or growth |
479 |
|
|
point for the rest of the edge to meet up, akin to that of a |
480 |
|
|
zipper. From the handful of cases where a double layer was formed |
481 |
|
|
during the simulation, measuring from the initial appearance of a |
482 |
|
|
growth point, the double layer tends to be fully formed within |
483 |
|
|
$\sim$~35 ns. |
484 |
|
|
|
485 |
jmichalk |
3862 |
There are a number of possible mechanisms to explain the role of |
486 |
|
|
adsorbed CO in restructuring the Pt surface. Quadrupolar repulsion |
487 |
|
|
between adjacent CO molecules adsorbed on the surface is one |
488 |
|
|
possibility. However, the quadrupole-quadrupole interaction is |
489 |
|
|
short-ranged and is attractive for some orientations. If the CO |
490 |
|
|
molecules are ``locked'' in a specific orientation relative to each other however, |
491 |
|
|
this explanation gains some weight. The energetic repulsion between two CO |
492 |
|
|
located a distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) with both in a |
493 |
|
|
vertical orientation is 8.62 kcal/mole. Moving the CO apart to the second nearest-neighbor |
494 |
|
|
distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to nearly 0 kcal/mole. SHOW A NUMBER FOR ROTATION. |
495 |
|
|
As mentioned above, the energy barrier for surface diffusion of a platinum adatom is only 4 kcal/mole. So this |
496 |
|
|
repulsion between CO can help increase the surface diffusion. However, the residence time of CO was examined |
497 |
|
|
and while the majority of the CO is on or near the surface throughout the run, it is extremely mobile. This mobility |
498 |
|
|
suggests that the CO are more likely to shift their positions without necessarily dragging the platinum along |
499 |
|
|
with them. |
500 |
|
|
|
501 |
|
|
Another possible and more likely mechanism for the restructuring is in the |
502 |
|
|
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
503 |
|
|
Pt atoms. This could have the effect of increasing surface mobility |
504 |
|
|
of these atoms. To test this hypothesis, numerous configurations of |
505 |
|
|
CO in varying quantities were arranged on the higher and lower plateaus |
506 |
|
|
around a step on a otherwise clean Pt (557) surface. One representative |
507 |
|
|
configuration is displayed in figure \ref{fig:lambda}. Single or concerted movement |
508 |
|
|
of platinum atoms was then examined to determine possible barriers. Because |
509 |
|
|
of the forced movement along a pre-defined reaction coordinate that may differ |
510 |
|
|
from the true minimum of this path, only the beginning and ending energies |
511 |
|
|
are displayed in table \ref{tab:energies}. The presence of CO at suitable |
512 |
|
|
sites can lead to lowered barriers for platinum breaking apart from the step edge. |
513 |
|
|
Additionally, as highlighted in figure \ref{fig:lambda}, the presence of CO makes the |
514 |
|
|
burrowing and lifting nature favorable, whereas without CO, the process is neutral |
515 |
|
|
in terms of energetics. |
516 |
|
|
|
517 |
|
|
%lambda progression of Pt -> shoving its way into the step |
518 |
|
|
\begin{figure}[H] |
519 |
|
|
\includegraphics[width=\linewidth]{lambdaProgression_atopCO.png} |
520 |
|
|
\caption{A model system of the Pt 557 surface was used as the framework for a reaction coordinate. |
521 |
|
|
Various numbers, placements, and rotations of CO were examined. The one displayed was a |
522 |
|
|
representative sample. As shown in Table , relative to the energy at 0\% there is a slight decrease |
523 |
|
|
upon insertion of the platinum atom into the step edge along with the resultant lifting of the other |
524 |
|
|
platinum atom.} |
525 |
|
|
\label{fig:lambda} |
526 |
|
|
\end{figure} |
527 |
|
|
|
528 |
|
|
|
529 |
|
|
|
530 |
jmichalk |
3802 |
\subsection{Diffusion} |
531 |
jmichalk |
3862 |
As shown in the results section, the diffusion parallel to the step edge tends to be |
532 |
|
|
much faster than that perpendicular to the step edge. Additionally, the coverage |
533 |
|
|
of CO appears to play a slight role in relative rates of diffusion, as shown in figure \ref{fig:diff} |
534 |
|
|
Thus, the bottleneck of the double layer formation appears to be the initial formation |
535 |
|
|
of this growth point, which seems to be somewhat of a stochastic event. Once it |
536 |
|
|
appears, parallel diffusion, along the now slightly angled step edge, will allow for |
537 |
|
|
a faster formation of the double layer than if the entire process were dependent on |
538 |
|
|
only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the |
539 |
|
|
more likely a growth point is to be formed. |
540 |
jmichalk |
3802 |
\\ |
541 |
jmichalk |
3862 |
|
542 |
|
|
|
543 |
|
|
%breaking of the double layer upon removal of CO |
544 |
jmichalk |
3802 |
\begin{figure}[H] |
545 |
jmichalk |
3862 |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
546 |
|
|
\caption{Hi} |
547 |
|
|
\label{fig:breaking} |
548 |
jmichalk |
3802 |
\end{figure} |
549 |
|
|
|
550 |
|
|
|
551 |
jmichalk |
3862 |
|
552 |
|
|
|
553 |
jmichalk |
3802 |
%Peaks! |
554 |
jmichalk |
3816 |
\begin{figure}[H] |
555 |
gezelter |
3826 |
\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
556 |
jmichalk |
3816 |
\caption{} |
557 |
jmichalk |
3862 |
\label{fig:peaks} |
558 |
jmichalk |
3816 |
\end{figure} |
559 |
jmichalk |
3862 |
|
560 |
|
|
%clean surface... |
561 |
jmichalk |
3827 |
\begin{figure}[H] |
562 |
|
|
\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
563 |
|
|
\caption{} |
564 |
jmichalk |
3862 |
|
565 |
jmichalk |
3827 |
\end{figure} |
566 |
jmichalk |
3862 |
\label{fig:clean} |
567 |
jmichalk |
3802 |
\section{Conclusion} |
568 |
|
|
|
569 |
|
|
|
570 |
jmichalk |
3862 |
%Things I am not ready to remove yet |
571 |
|
|
|
572 |
|
|
%Table of Diffusion Constants |
573 |
|
|
%Add gold?M |
574 |
|
|
% \begin{table}[H] |
575 |
|
|
% \caption{} |
576 |
|
|
% \centering |
577 |
|
|
% \begin{tabular}{| c | cc | cc | } |
578 |
|
|
% \hline |
579 |
|
|
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
580 |
|
|
% \hline |
581 |
|
|
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
582 |
|
|
% \hline |
583 |
|
|
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
584 |
|
|
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
585 |
|
|
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
586 |
|
|
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
587 |
|
|
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
588 |
|
|
% \hline |
589 |
|
|
% \end{tabular} |
590 |
|
|
% \end{table} |
591 |
|
|
|
592 |
gezelter |
3808 |
\section{Acknowledgments} |
593 |
|
|
Support for this project was provided by the National Science |
594 |
|
|
Foundation under grant CHE-0848243 and by the Center for Sustainable |
595 |
|
|
Energy at Notre Dame (cSEND). Computational time was provided by the |
596 |
|
|
Center for Research Computing (CRC) at the University of Notre Dame. |
597 |
jmichalk |
3802 |
|
598 |
gezelter |
3808 |
\newpage |
599 |
|
|
\bibliography{firstTryBibliography} |
600 |
|
|
\end{doublespace} |
601 |
|
|
\end{document} |