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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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|
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\author{Joseph R. Michalka} |
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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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%% |
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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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|
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|
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\begin{abstract} |
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We examine surface reconstructions of Pt and Au(557) under |
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various CO coverages using molecular dynamics in order to |
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explore possible mechanisms for any observed reconstructions |
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and their dynamics. The metal-CO interactions were parameterized |
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as part of this work so that an efficient large-scale treatment of |
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this system could be undertaken. The large difference in binding |
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strengths of the metal-CO interactions was found to play a significant |
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role with regards to step-edge stability and adatom diffusion. A |
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small correlation between coverage and the diffusion constant |
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was also determined. The energetics of CO adsorbed to the surface |
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is sufficient to explain the reconstructions observed on the Pt |
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systems and the lack of reconstruction of the Au systems. |
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|
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|
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The mechanism and dynamics of surface reconstructions of Pt(557) |
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and Au(557) exposed to various coverages of carbon monoxide (CO) |
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were investigated using molecular dynamics simulations. Metal-CO |
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interactions were parameterized from experimental data and plane-wave |
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Density Functional Theory (DFT) calculations. The large difference in |
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binding strengths of the Pt-CO and Au-CO interactions was found to play |
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a significant role in step-edge stability and adatom diffusion constants. |
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The energetics of CO adsorbed to the surface is sufficient to explain the |
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step-doubling reconstruction observed on Pt(557) and the lack of such |
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a reconstruction on the Au(557) surface. |
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\end{abstract} |
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|
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\newpage |
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|
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|
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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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|
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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) |
132 |
surface restructuring using molecular simulations. Since the dynamics |
133 |
of the process are of particular interest, we employ classical force |
134 |
fields that represent a compromise between chemical accuracy and the |
135 |
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 |
137 |
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 |
143 |
reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the |
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22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
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become adatoms, limiting the stress of this reconstruction, while |
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allowing the rest to relax and approach the ideal (111) |
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configuration. They did not see the usual herringbone pattern on Au(111) being greatly |
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affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a |
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disruption of the herringbone pattern as CO was adsorbed to the |
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surface. Both groups suggested that the preference CO shows for |
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low-coordinated Au atoms was the primary driving force for the reconstruction. |
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|
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|
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|
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%Platinum molecular dynamics |
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%gold molecular dynamics |
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|
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\section{Simulation Methods} |
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The challenge in modeling any solid/gas interface 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 |
172 |
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 |
175 |
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 |
177 |
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 |
183 |
density. The embedded atom method (EAM) is perhaps the best known of |
184 |
these |
185 |
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 |
187 |
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
188 |
parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the |
189 |
fastest of these density functional approaches. In |
190 |
all of these models, atoms are treated as a positively charged |
191 |
core with a radially-decaying valence electron distribution. To |
192 |
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 |
194 |
atomic sites is computed at atom $i$'s location, |
195 |
\begin{equation*} |
196 |
\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}) |
197 |
\end{equation*} |
198 |
Here, $\rho_j(r_{ij})$ is the function that describes the distance |
199 |
dependence of the valence electron distribution of atom $j$. The |
200 |
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*} |
203 |
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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|
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The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
219 |
have all been widely used by the materials simulation community for |
220 |
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 |
232 |
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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|
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|
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|
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|
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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} |
244 |
We used a model first proposed by Karplus and Straub to study |
245 |
the photodissociation of CO from myoglobin because it reproduces |
246 |
the quadrupole moment well.\cite{Straub} The Straub and |
247 |
Karplus model treats CO as a rigid three site molecule with a massless M |
248 |
site at the molecular center of mass. The geometry and interaction |
249 |
parameters are reproduced in Table~\ref{tab:CO}. The effective |
250 |
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 |
252 |
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
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mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
254 |
%CO Table |
255 |
\begin{table}[H] |
256 |
\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
257 |
$\epsilon$), and charges for the CO-CO |
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interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
259 |
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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|
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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 |
288 |
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 |
293 |
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. |
303 |
Adsorption energies were obtained from gas-surface DFT calculations with a |
304 |
periodic supercell plane-wave basis approach, as implemented in the |
305 |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
306 |
described with the projector augmented-wave (PAW) |
307 |
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 |
309 |
computed with the PBE implementation of the generalized gradient |
310 |
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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In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
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Au x 2 Au surface planes and separated from vertical images by six |
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layers of vacuum space. The surface atoms were all allowed to relax |
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before CO was added to the system. Electronic relaxations were |
316 |
performed until the energy difference between subsequent steps |
317 |
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
318 |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
319 |
zone.\cite{Monkhorst:1976} The relaxed gold slab was |
320 |
then used in numerous single point calculations with CO at various |
321 |
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 for the metal-CO cross-interactions in this work |
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are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
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(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
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and polarization are neglected in this model, although these effects could have |
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an effect on binding energies and binding site preferences. |
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|
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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 |
336 |
interactions are modeled with Lennard-Jones potentials. While the |
337 |
metal-O interactions were fit to Morse |
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potentials. Distances are given in \AA~and energies in kcal/mol. } |
339 |
\centering |
340 |
\begin{tabular}{| c | cc | c | ccc |} |
341 |
\hline |
342 |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\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\\ |
346 |
|
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\hline |
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\end{tabular} |
349 |
\label{tab:co_parameters} |
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\end{table} |
351 |
|
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%Table of energies |
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\begin{table}[H] |
354 |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
355 |
described in this work. All values are in eV.} |
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\centering |
357 |
\begin{tabular}{| c | cc |} |
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\hline |
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& Calculated & Experimental \\ |
360 |
\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}) \\ |
363 |
& & -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{TPDGold}) \\ |
365 |
\hline |
366 |
\end{tabular} |
367 |
\label{tab:co_energies} |
368 |
\end{table} |
369 |
|
370 |
\subsection{Pt(557) and Au(557) metal interfaces} |
371 |
Our Pt system is an orthorhombic periodic box of dimensions |
372 |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
373 |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
374 |
are 9 and 8 atoms deep respectively, corresponding to a slab |
375 |
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
376 |
The systems are arranged in a FCC crystal that have been cut |
377 |
along the (557) plane so that they are periodic in the {\it x} and |
378 |
{\it y} directions, and have been oriented to expose two aligned |
379 |
(557) cuts along the extended {\it z}-axis. Simulations of the |
380 |
bare metal interfaces at temperatures ranging from 300~K to |
381 |
1200~K were performed to confirm the relative |
382 |
stability of the surfaces without a CO overlayer. |
383 |
|
384 |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
385 |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
386 |
different temperatures for the two metals. The bare Au and Pt surfaces were |
387 |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
388 |
respectively for 100 ps. The two surfaces were relatively stable at these |
389 |
temperatures when no CO was present, but experienced increased surface |
390 |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
391 |
that was initially placed in the vacuum region. Upon full adsorption, |
392 |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
393 |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
394 |
which introduces artifacts that are not relevant to (557) reconstruction. |
395 |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
396 |
the Au surfaces often had a significant CO population in the gas |
397 |
phase. These systems were allowed to reach thermal equilibrium (over |
398 |
5~ns) before being run in the microcanonical (NVE) ensemble for |
399 |
data collection. All of the systems examined had at least 40~ns in the |
400 |
data collection stage, although simulation times for some Pt of the |
401 |
systems exceeded 200~ns. Simulations were carried out using the open |
402 |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
403 |
|
404 |
|
405 |
|
406 |
|
407 |
% RESULTS |
408 |
% |
409 |
\section{Results} |
410 |
\subsection{Structural remodeling} |
411 |
The bare metal surfaces experienced minor roughening of the |
412 |
step-edge because of the elevated temperatures, but the (557) |
413 |
face was stable throughout the simulations. The surface of both |
414 |
systems, upon dosage of CO, began to undergo extensive remodeling |
415 |
that was not observed in the bare systems. Reconstructions of |
416 |
the Au systems were limited to breakup of the step-edges and |
417 |
some step wandering. The lower coverage Pt systems experienced |
418 |
similar restructuring but to a greater extent. The 50\% coverage |
419 |
Pt system was unique among our simulations in that it formed |
420 |
well-defined and stable double layers through step coalescence, |
421 |
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
422 |
|
423 |
|
424 |
\subsubsection{Step wandering} |
425 |
The 0\% coverage surfaces for both metals showed minimal |
426 |
step-wandering at their respective temperatures. As the CO |
427 |
coverage increased however, the mobility of the surface atoms, |
428 |
described through adatom diffusion and step-edge wandering, |
429 |
also increased. Except for the 50\% Pt system where step |
430 |
coalescence occurred, the step-edges in the other simulations |
431 |
preferred to keep nearly the same distance between steps as in |
432 |
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
433 |
Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
434 |
highlights the repulsion that exists between step-edges even |
435 |
when no direct interactions are present in the system. This |
436 |
repulsion is caused by an entropic barrier that arises from |
437 |
the fact that steps cannot cross over one another. This entropic |
438 |
repulsion does not completely define the interactions between |
439 |
steps, however, so it is possible to observe step coalescence |
440 |
on some surfaces.\cite{Williams:1991} The presence and |
441 |
concentration of adsorbates, as shown in this work, can |
442 |
affect step-step interactions, potentially leading to a new |
443 |
surface structure as the thermodynamic equilibrium. |
444 |
|
445 |
\subsubsection{Double layers} |
446 |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
447 |
undergoes two separate reconstructions upon CO adsorption. |
448 |
The first involves a doubling of the step height and plateau length. |
449 |
Similar behavior has been seen on a number of surfaces |
450 |
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
451 |
Of the two systems we examined, the Pt system showed a greater |
452 |
propensity for reconstruction |
453 |
because of the larger surface mobility and the greater extent of step wandering. |
454 |
The amount of reconstruction was strongly correlated to the amount of CO |
455 |
adsorbed upon the surface. This appears to be related to the |
456 |
effect that adsorbate coverage has on edge breakup and on the |
457 |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
458 |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
459 |
Over a longer time scale (150~ns) two more double layers formed |
460 |
on this surface. Although double layer formation did not occur |
461 |
in the other Pt systems, they exhibited more step-wandering and |
462 |
roughening compared to their Au counterparts. The |
463 |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
464 |
various times along the simulation showing the evolution of a double layer step-edge. |
465 |
|
466 |
The second reconstruction observed by |
467 |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
468 |
across the plateau between two step-edges. Neither metal, within |
469 |
the 40~ns time scale or the extended simulation time of 150~ns for |
470 |
the 50\% Pt system, experienced this reconstruction. |
471 |
|
472 |
%Evolution of surface |
473 |
\begin{figure}[H] |
474 |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
475 |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
476 |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
477 |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
478 |
doubling of the layers appears only after two adjacent step-edges |
479 |
touch. The circled spot in (b) nucleated the growth of the double |
480 |
step observed in the later configurations.} |
481 |
\label{fig:reconstruct} |
482 |
\end{figure} |
483 |
|
484 |
\subsection{Dynamics} |
485 |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
486 |
using STM, has been able to capture the coalescence of steps |
487 |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
488 |
provides an upper bound for the time required for the doubling |
489 |
to occur. By utilizing Molecular Dynamics we are able to probe |
490 |
the dynamics of these reconstructions at elevated temperatures |
491 |
and in this section we provide data on the timescales for transport |
492 |
properties, e.g. diffusion and layer formation time. |
493 |
|
494 |
|
495 |
\subsubsection{Transport of surface metal atoms} |
496 |
%forcedSystems/stepSeparation |
497 |
The wandering of a step-edge is a cooperative effect |
498 |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
499 |
displaying a low index facet, (111) or (100), is unlikely to experience |
500 |
much surface diffusion because of the large energetic barrier that must |
501 |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
502 |
on higher-index facets provides a lower energy source for mobile metal atoms. |
503 |
Single-atom break-away from a step-edge on a clean surface still imposes an |
504 |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
505 |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
506 |
The penalty lowers significantly when CO is present in sufficient quantities |
507 |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
508 |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
509 |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
510 |
able to explore the terrace before rejoining either their original step-edge or |
511 |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
512 |
to traverse to a separate terrace although the presence of CO can lower the |
513 |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
514 |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
515 |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
516 |
observation of the mobile metal atoms showed that they were typically in |
517 |
equilibrium with the step-edges. |
518 |
At times, their motion was concerted and two or more adatoms would be |
519 |
observed moving together across the surfaces. |
520 |
|
521 |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
522 |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
523 |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
524 |
was used to prevent swamping the diffusion data with the in-place vibrational |
525 |
movement of buried atoms. Diffusion on a surface is strongly affected by |
526 |
local structures and in this work, the presence of single and double layer |
527 |
step-edges causes the diffusion parallel to the step-edges to be larger than |
528 |
the diffusion perpendicular to these edges. Parallel and perpendicular |
529 |
diffusion constants are shown in Figure \ref{fig:diff}. |
530 |
|
531 |
%Diffusion graph |
532 |
\begin{figure}[H] |
533 |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
534 |
\caption{Diffusion constants for mobile surface atoms along directions |
535 |
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
536 |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
537 |
surface coverage. Diffusion parallel to the step-edge is higher |
538 |
than that perpendicular to the edge because of the lower energy |
539 |
barrier associated with traversing along the edge as compared to |
540 |
completely breaking away. The two reported diffusion constants for |
541 |
the 50\% Pt system arise from different sample sets. The lower values |
542 |
correspond to the same 40~ns amount that all of the other systems were |
543 |
examined at, while the larger values correspond to a 20~ns period } |
544 |
\label{fig:diff} |
545 |
\end{figure} |
546 |
|
547 |
The weaker Au-CO interaction is evident in the weak CO-coverage |
548 |
dependance of Au diffusion. This weak interaction leads to lower |
549 |
observed coverages when compared to dosage amounts. This further |
550 |
limits the effect the CO can have on surface diffusion. The correlation |
551 |
between coverage and Pt diffusion rates shows a near linear relationship |
552 |
at the earliest times in the simulations. Following double layer formation, |
553 |
however, there is a precipitous drop in adatom diffusion. As the double |
554 |
layer forms, many atoms that had been tracked for mobility data have |
555 |
now been buried resulting in a smaller reported diffusion constant. A |
556 |
secondary effect of higher coverages is CO-CO cross interactions that |
557 |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
558 |
This effect would become evident only at higher coverages. A detailed |
559 |
account of Pt adatom energetics follows in the Discussion. |
560 |
|
561 |
|
562 |
\subsubsection{Dynamics of double layer formation} |
563 |
The increased diffusion on Pt at the higher CO coverages is the primary |
564 |
contributor to double layer formation. However, this is not a complete |
565 |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
566 |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
567 |
system, one double layer formed within the first 40~ns of simulation time, |
568 |
while two more were formed as the system was allowed to run for an |
569 |
additional 110~ns (150~ns total). This suggests that this reconstruction |
570 |
is a rapid process and that the previously mentioned upper bound is a |
571 |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
572 |
appearance of a double layer appears at 19~ns into the simulation. |
573 |
Within 12~ns of this nucleation event, nearly half of the step has formed |
574 |
the double layer and by 86~ns the complete layer has flattened out. |
575 |
From the appearance of the first nucleation event to the first observed |
576 |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
577 |
necessary for the layer to completely straighten. The other two layers in |
578 |
this simulation formed over periods of 22~ns and 42~ns respectively. |
579 |
A possible explanation for this rapid reconstruction is the elevated |
580 |
temperatures under which our systems were simulated. The process |
581 |
would almost certainly take longer at lower temperatures. Additionally, |
582 |
our measured times for completion of the doubling after the appearance |
583 |
of a nucleation site are likely affected by our periodic boxes. A longer |
584 |
step-edge will likely take longer to ``zipper''. |
585 |
|
586 |
|
587 |
%Discussion |
588 |
\section{Discussion} |
589 |
We have shown that a classical potential model is able to model the |
590 |
initial reconstruction of the Pt(557) surface upon CO adsorption as |
591 |
shown by Tao {\it et al}.\cite{Tao:2010}. More importantly, we were |
592 |
able to observe features of the dynamic processes necessary for |
593 |
this reconstruction. Here we discuss the features of the model that |
594 |
give rise to the observed dynamical properties of the (557) reconstruction. |
595 |
|
596 |
\subsection{Diffusion} |
597 |
The perpendicular diffusion constant |
598 |
appears to be the most important indicator of double layer |
599 |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
600 |
formation of the double layer did not begin until a nucleation |
601 |
site appeared. And as mentioned by Williams {\it et al}.\cite{Williams:1991, Williams:1994}, |
602 |
the inability for edges to cross leads to an effective edge-edge repulsion that |
603 |
must be overcome to allow step coalescence. |
604 |
A greater $\textbf{D}_\perp$ implies more step-wandering |
605 |
and a larger chance for the stochastic meeting of two edges |
606 |
to create a nucleation point. Parallel diffusion along the step-edge can help ``zipper'' up a nascent double |
607 |
layer. This helps explain why the time scale for formation after |
608 |
the appearance of a nucleation site was rapid, while the initial |
609 |
appearance of the nucleation site was unpredictable. |
610 |
|
611 |
\subsection{Mechanism for restructuring} |
612 |
Since the Au surface showed no large scale restructuring in any of |
613 |
our simulations, our discussion will focus on the 50\% Pt-CO system |
614 |
which did exhibit doubling. A |
615 |
number of possible mechanisms exist to explain the role of adsorbed |
616 |
CO in restructuring the Pt surface. Quadrupolar repulsion between |
617 |
adjacent CO molecules adsorbed on the surface is one possibility. |
618 |
However, the quadrupole-quadrupole interaction is short-ranged and |
619 |
is attractive for some orientations. If the CO molecules are ``locked'' in |
620 |
a specific orientation relative to each other, through atop adsorption for |
621 |
example, this explanation would gain credence. The calculated energetic repulsion |
622 |
between two CO molecules located a distance of 2.77~\AA~apart |
623 |
(nearest-neighbor distance of Pt) and both in a vertical orientation, |
624 |
is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance |
625 |
of 4.8~\AA~drops the repulsion to nearly 0. Allowing the CO to rotate away |
626 |
from a purely vertical orientation also lowers the repulsion. When the |
627 |
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is |
628 |
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. |
629 |
The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
630 |
repulsion between adjacent CO molecules bound to Pt could increase the surface |
631 |
diffusion. However, the residence time of CO on Pt suggests that these |
632 |
molecules are extremely mobile, with diffusion constants 40 to 2500 times |
633 |
larger than surface Pt atoms. This mobility suggests that the CO molecules jump |
634 |
between different Pt atoms throughout the simulation, but will stay bound for |
635 |
significant periods of time. |
636 |
|
637 |
A different interpretation of the above mechanism, taking into account the large |
638 |
mobility of the CO, looks at how instantaneous and short-lived configurations of |
639 |
CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge |
640 |
breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach |
641 |
an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
642 |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases |
643 |
(e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances, |
644 |
it becomes quite energetically favorable to roughen the edge by introducing a small |
645 |
separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in |
646 |
simulations with significant CO populations. The roughening is present to a lesser extent |
647 |
on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely |
648 |
due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism |
649 |
of step-edge breakup suggested by these energy curves is one of the most difficult |
650 |
processes, a complete break-away from the step-edge in one unbroken movement. |
651 |
Easier multistep mechanisms likely exist where an adatom moves laterally on the surface |
652 |
after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest |
653 |
neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher |
654 |
than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO |
655 |
quadrupolar repulsion is still playing a primary role, but for its importance in roughening |
656 |
the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not |
657 |
born out by their mobility data. The requirement for a large density of CO on the surface |
658 |
for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic} |
659 |
correspond well with the increased mobility seen on higher coverage surfaces. |
660 |
|
661 |
%Sketch graphic of different configurations |
662 |
\begin{figure}[H] |
663 |
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
664 |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
665 |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
666 |
upon them. These are a sampling of the configurations examined to gain a more |
667 |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
668 |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
669 |
\label{fig:SketchGraphic} |
670 |
\end{figure} |
671 |
|
672 |
%energy graph corresponding to sketch graphic |
673 |
\begin{figure}[H] |
674 |
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf} |
675 |
\caption{The energy curves directly correspond to the labeled model |
676 |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
677 |
to their initial configuration so the energy of a and h do not have the |
678 |
same zero value. As is seen, certain arrangements of CO can lower |
679 |
the energetic barrier that must be overcome to create an adatom. |
680 |
However, it is the highest coverages where these higher-energy |
681 |
configurations of CO will be more likely. } |
682 |
\label{fig:SketchEnergies} |
683 |
\end{figure} |
684 |
|
685 |
While configurations of CO on the surface are able to increase diffusion, |
686 |
this does not immediately provide an explanation for the formation of double |
687 |
layers. If adatoms were constrained to their terrace then doubling would be |
688 |
much less likely to occur. Nucleation sites could still potentially form, but there |
689 |
would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the |
690 |
step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in |
691 |
our simulations with our periodic treatment of the system, the system is not large enough to experience this effect. |
692 |
Thus, there must be a mechanism that explains how adatoms are able to move |
693 |
amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate |
694 |
where an adatom along the step-edge with an adsorbed CO ``burrows'' into the |
695 |
edge displacing an atom onto the higher terrace. This mechanism was chosen |
696 |
because of similar events that were observed during the simulations. The barrier |
697 |
heights we obtained are only approximations because we constrained the movement |
698 |
of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s |
699 |
are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and |
700 |
this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown |
701 |
in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. |
702 |
While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol |
703 |
difference in energies and makes the process energetically favorable. |
704 |
|
705 |
%lambda progression of Pt -> shoving its way into the step |
706 |
\begin{figure}[H] |
707 |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
708 |
\caption{ Various points along a reaction coordinate are displayed in the figure. |
709 |
The mechanism of edge traversal is examined in the presence of CO. The approximate |
710 |
barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process |
711 |
is -15~kcal/mol making it an energetically favorable process.} |
712 |
\label{fig:lambda} |
713 |
\end{figure} |
714 |
|
715 |
The mechanism for doubling on this surface appears to require the cooperation of at least |
716 |
these two described processes. For complete doubling of a layer to occur there must |
717 |
be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from |
718 |
that terrace they must either rise up on the ledge above them or drop to the ledge below |
719 |
them. The presence of CO helps with the energetics of both of these situations. There must be sufficient |
720 |
breakage of the step-edge to increase the concentration of adatoms on the surface and |
721 |
these adatoms must then undergo the burrowing highlighted above or some comparable |
722 |
mechanism to traverse the step-edge. Over time, these mechanisms working in concert |
723 |
lead to the formation of a double layer. |
724 |
|
725 |
\subsection{CO Removal and double layer stability} |
726 |
Once a double layer had formed on the 50\%~Pt system it |
727 |
remained for the rest of the simulation time with minimal |
728 |
movement. There were configurations that showed small |
729 |
wells or peaks forming, but typically within a few nanoseconds |
730 |
the feature would smooth away. Within our simulation time, |
731 |
the formation of the double layer was irreversible and a double |
732 |
layer was never observed to split back into two single layer |
733 |
step-edges while CO was present. To further gauge the effect |
734 |
CO had on this system, additional simulations were run starting |
735 |
from a late configuration of the 50\%~Pt system that had formed |
736 |
double layers. These simulations then had their CO removed. |
737 |
The double layer breaks rapidly in these simulations, already |
738 |
showing a well-defined splitting after 100~ps. Configurations of |
739 |
this system are shown in Figure \ref{fig:breaking}. The coloring |
740 |
of the top and bottom layers helps to exhibit how much mixing |
741 |
the edges experience as they split. These systems were only |
742 |
examined briefly, 10~ns, and within that time despite the initial |
743 |
rapid splitting, the edges only moved another few \AA~apart. |
744 |
It is possible with longer simulation times that the |
745 |
(557) lattice could be recovered as seen by Tao {\it et al}.\cite{Tao:2010} |
746 |
|
747 |
|
748 |
|
749 |
%breaking of the double layer upon removal of CO |
750 |
\begin{figure}[H] |
751 |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
752 |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
753 |
helped maintain the stability of the double layer and its microfaceting of the double layer |
754 |
into a (111) configuration. This microfacet immediately reverts to the original (100) step |
755 |
edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather |
756 |
there is a mixing of the lower and upper atoms at the edge.} |
757 |
\label{fig:breaking} |
758 |
\end{figure} |
759 |
|
760 |
|
761 |
|
762 |
|
763 |
%Peaks! |
764 |
%\begin{figure}[H] |
765 |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
766 |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
767 |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
768 |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
769 |
%\label{fig:peaks} |
770 |
%\end{figure} |
771 |
|
772 |
|
773 |
%Don't think I need this |
774 |
%clean surface... |
775 |
%\begin{figure}[H] |
776 |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
777 |
%\caption{} |
778 |
|
779 |
%\end{figure} |
780 |
%\label{fig:clean} |
781 |
|
782 |
|
783 |
\section{Conclusion} |
784 |
The strength of the Pt-CO binding interaction as well as the large |
785 |
quadrupolar repulsion between CO molecules are sufficient to |
786 |
explain the observed increase in surface mobility and the resultant |
787 |
reconstructions at the highest simulated coverage. The weaker |
788 |
Au-CO interaction results in lower diffusion constants, less step-wandering, |
789 |
and a lack of the double layer reconstruction. An in-depth examination |
790 |
of the energetics shows the important role CO plays in increasing |
791 |
step-breakup and in facilitating edge traversal which are both |
792 |
necessary for double layer formation. |
793 |
|
794 |
|
795 |
|
796 |
%Things I am not ready to remove yet |
797 |
|
798 |
%Table of Diffusion Constants |
799 |
%Add gold?M |
800 |
% \begin{table}[H] |
801 |
% \caption{} |
802 |
% \centering |
803 |
% \begin{tabular}{| c | cc | cc | } |
804 |
% \hline |
805 |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
806 |
% \hline |
807 |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
808 |
% \hline |
809 |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
810 |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
811 |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
812 |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
813 |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
814 |
% \hline |
815 |
% \end{tabular} |
816 |
% \end{table} |
817 |
|
818 |
\begin{acknowledgement} |
819 |
Support for this project was provided by the National Science |
820 |
Foundation under grant CHE-0848243 and by the Center for Sustainable |
821 |
Energy at Notre Dame (cSEND). Computational time was provided by the |
822 |
Center for Research Computing (CRC) at the University of Notre Dame. |
823 |
\end{acknowledgement} |
824 |
\newpage |
825 |
\bibliography{firstTryBibliography} |
826 |
%\end{doublespace} |
827 |
|
828 |
\begin{tocentry} |
829 |
%\includegraphics[height=3.5cm]{timelapse} |
830 |
\end{tocentry} |
831 |
|
832 |
\end{document} |