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\title{Molecular Dynamics simulations of the surface reconstructions |
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of Pt(557) and Au(557) under exposure to CO} |
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\author{Joseph R. Michalka} |
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\author{Patrick W. McIntyre} |
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\author{J. Daniel Gezelter} |
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\email{gezelter@nd.edu} |
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\affiliation[University of Notre Dame]{251 Nieuwland Science Hall\\ |
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Department of Chemistry and Biochemistry\\ University of Notre |
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Dame\\ Notre Dame, Indiana 46556} |
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\keywords{} |
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\begin{document} |
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%% |
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%Introduction |
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% Experimental observations |
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%% |
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\begin{abstract} |
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The mechanism and dynamics of surface reconstructions of Pt(557) and |
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Au(557) exposed to various coverages of carbon monoxide (CO) were |
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investigated using molecular dynamics simulations. Metal-CO |
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interactions were parameterized from experimental data and |
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plane-wave Density Functional Theory (DFT) calculations. The large |
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difference in binding strengths of the Pt-CO and Au-CO interactions |
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was found to play a significant role in step-edge stability and |
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adatom diffusion constants. Various mechanisms for CO-mediated step |
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wandering and step doubling were investigated on the Pt(557) |
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surface. We find that the energetics of CO adsorbed to the surface |
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can explain the step-doubling reconstruction observed on Pt(557) and |
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the lack of such a reconstruction on the Au(557) surface. |
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\end{abstract} |
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\begin{document} |
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%Title |
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\title{Investigation of the Pt and Au 557 Surface Reconstructions under a CO Atmosphere} |
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%Date |
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\date{Dec 15, 2012} |
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%authors |
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\author{Joseph R.~Michalka, Patrick W. McIntyre, \& J.~Daniel Gezelter} |
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% make the title |
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\maketitle |
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\newpage |
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\doublespacing |
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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: 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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High-index surfaces of catalytically active metals are an important area of exploration because they are typically more reactive than an ideal surface of the same metal. The greater number of low-coordinated surface atoms is believed responsible for this increased reactivity \cite{}. Additionally, the activity and specificity of many metals towards certain chemical processes has been shown to strongly depend on the structure of the surface \cite{}. Prior work has also shown that reaction conditions, such as high pressures and high temperatures are able to cause reconstructions of the metallic surface, either through changing the displayed surface facets or by changing the number and types of high-index sites available for reactions \cite{doi:10.1126/science.1197461,doi:10.1021/nn3015322, doi:10.1021/jp302379x}. A greater understanding of these high-index surfaces and the restructuring processes they undergo is needed as a prerequisite for more intelligent catalyst design. While current experimental work has started exploring systems at \emph{in situ} conditions, for a long time such experiments were limited to ideal surfaces in high vacuum. New techniques, such as ambient pressure XPS (AP-XPS) \cite{}, high-pressure XPS (HP-XPS) \cite{}, high-pressure STM \cite{}, environmental transmission electron microscopy (E-TEM) \cite{} and many others, are providing clearer pictures of the processes that are occurring on metal surfaces under these conditions. Nevertheless, all of these techniques still have limitations, especially in observing what is occurring at an atomic level. Theoretical models and simulations in combination with experiment have proven their worth in explaining the underlying reasons for some of these reconstructions \cite{}. |
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\\ |
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By examining two different metal-CO systems the effect that the metal and the metal-CO interaction plays can be elucidated. Our first system is composed of platinum and CO and has been the subject of many experimental and theoretical studies primarily because of platinum's strong reactivity toward CO oxidation. The focus has primarily been on adsorption energies, preferred adsorption sites, and catalytic activities. The second system we examined is composed of gold and CO. The gold-CO interaction is much weaker than the platinum-CO interaction and it seems likely that this difference in attraction would lead to differences in any potential surface reconstructions. |
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%It has also been a good test for new quantum methods because of the difficulty with modeling the preference CO has for the atop binding site \cite{doi:10.1021/jp002302t}. |
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%Now that dynamic surface events are known to play a role in many catalytic systems, additional research is being done to more closely examine many systems. Recent work by Tao et al. \cite{doi:10.1126/science.1182122} shows that a high-index platinum surface undergoes surface reconstructions when exposed to a small amount of CO, $\sim$~1 torr. Unexpectedly, the reconstruction was metastable and reverted upon removal of the CO. Work by McCarthy et al. \cite{doi:10.1021/jp302379x} examined temperature programmed desorption's of CO from various platinum samples and saw that species which had large amounts of low-coordinated surface atoms, highly sputtered surfaces or small nano particles, developed a higher temperature desorption peak, suggesting that binding of CO to the platinum surface is strongly dependent on local geometry. |
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This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557) |
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surface restructuring using molecular simulations. Since the dynamics |
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of the process are of particular interest, we employ classical force |
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fields that represent a compromise between chemical accuracy and the |
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computational efficiency necessary to simulate the process of interest. |
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Since restructuring typically occurs as a result of specific interactions of the |
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catalyst with adsorbates, in this work, two metal systems exposed |
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to carbon monoxide were examined. The Pt(557) surface has already been shown |
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to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
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The Au(557) surface, because of a weaker interaction with CO, is less |
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likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000} |
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and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced |
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reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the |
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22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
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become adatoms, limiting the stress of this reconstruction, while |
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allowing the rest to relax and approach the ideal (111) |
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configuration. They did not see the usual herringbone pattern on Au(111) being greatly |
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affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a |
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disruption of the herringbone pattern as CO was adsorbed to the |
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surface. Both groups suggested that the preference CO shows for |
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low-coordinated Au atoms was the primary driving force for the reconstruction. |
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%Platinum molecular dynamics |
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%gold molecular dynamics |
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\section{Simulation Methods} |
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Our model systems are composed of approximately 4000 metal atoms cut along the 557 plane. The bare crystals were initially run in the Canonical ensemble at 1000K and 800K respectively for Pt and Au. The difference in temperature is necessary because of the two metals different melting points. Various amounts of CO were added to the simulation box and allowed to absorb to the metal surfaces over a short period of 100 ps. After further thermal relaxation the simulations were all run for at least 40 ns. A subset of the runs that showed interesting effects were allowed to run longer. The system |
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The challenge in modeling any solid/gas interface is the |
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development of a sufficiently general yet computationally tractable |
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model of the chemical interactions between the surface atoms and |
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adsorbates. Since the interfaces involved are quite large (10$^3$ - |
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10$^4$ atoms) and respond slowly to perturbations, {\it ab initio} |
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molecular dynamics |
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(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
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methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
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mechanical potential energy surfaces remain out of reach. |
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Additionally, the ``bonds'' between metal atoms at a surface are |
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typically not well represented in terms of classical pairwise |
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interactions in the same way that bonds in a molecular material are, |
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nor are they captured by simple non-directional interactions like the |
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Coulomb potential. For this work, we have used classical molecular |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid |
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three-site model developed by Straub and Karplus for studying |
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photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
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Pt-CO cross interactions were parameterized as part of this work. |
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|
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\subsection{Metal-metal interactions} |
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Many of the potentials used for modeling transition metals are based |
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on a non-pairwise additive functional of the local electron |
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density. The embedded atom method (EAM) is perhaps the best known of |
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these |
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methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
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but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
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the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
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parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the |
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fastest of these density functional approaches. In |
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all of these models, atoms are treated as a positively charged |
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core with a radially-decaying valence electron distribution. To |
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calculate the energy for embedding the core at a particular location, |
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the electron density due to the valence electrons at all of the other |
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atomic sites is computed at atom $i$'s location, |
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\begin{equation*} |
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\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}) |
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\end{equation*} |
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Here, $\rho_j(r_{ij})$ is the function that describes the distance |
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dependence of the valence electron distribution of atom $j$. The |
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contribution to the potential that comes from placing atom $i$ at that |
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location is then |
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\begin{equation*} |
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V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
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\end{equation*} |
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where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
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$\phi_{ij}(r_{ij})$ is a pairwise term that is meant to represent the |
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repulsive overlap of the two positively charged cores. |
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|
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% The {\it modified} embedded atom method (MEAM) adds angular terms to |
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% the electron density functions and an angular screening factor to the |
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% pairwise interaction between two |
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% atoms.\cite{BASKES:1994fk,Lee:2000vn,Thijsse:2002ly,Timonova:2011ve} |
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% MEAM has become widely used to simulate systems in which angular |
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% interactions are important (e.g. silicon,\cite{Timonova:2011ve} bcc |
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% metals,\cite{Lee:2001qf} and also interfaces.\cite{Beurden:2002ys}) |
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% MEAM presents significant additional computational costs, however. |
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|
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Our model systems are composed of approximately 4000 metal atoms cut along the 557 plane. This cut creates a stepped surface of 6x(111) surface plateaus separated by a single (100) atomic step height. The abundance of low-coordination atoms along the step edges acts as a suitable model for industrial catalysts which tend to have a high concentration of high-index sites. Experimental work has shown that such surfaces are notable for reconstructing upon adsorption\cite{}. Reconstructions have been seen for the Pt 557 surface that involve doubling of the step height and further formation of nano clusters with a triangular motif \cite{doi:10.1126/science.1182122}. To shed insight on whether this reconstruction is limited to the platinum surface, simulations of gold under similar conditions will also be examined. To properly observe these changes, our system size needs to be greater than the periodic phenomena we are examining. The large size and the long time scales needed precluded us from using quantum approaches. Thus, a forcefield describing the Metal-Metal, CO-CO, and CO-Metal interactions was parameterized and the simulations were run using OpenMD\cite{} an open-source molecular dynamics package. |
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%Metal |
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\subsection{Metal} |
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Recent metallic forcefields, inspired by density-functional theory, including EAM\cite{doi:10.1103/PhysRevB.29.6443, doi:10.1103/PhysRevB.33.7983} and QSC\cite{} have become very popular for modeling novel metallic systems. What makes these forcefields more suitable for metals than their pair-wise predecessors is that they work with the total electron density of the system in a manner akin to DFT. The energy contributed by a single atom is a function of the total background electron density at the point where the atom is to be embedded. The density at any given point is well-approximated by a linear superposition of the electron density as contributed by all the other atoms in the system. The function describing the energy as related to the density is parameterized for each element, rather than by solving the Kohn-Sham equations which is what allows this method to be used for large systems. The embedding energy is completely enclosed within the functional $F_i[\rho_{h,i}]$ which is dependent on the host density $\rho_{h}$ at atom $i$. The density at $i$ is the sum of the density as generated by the rest of the metal. The $\phi_{ij}$ term is a purely repulsive pair-pair interaction parameterized from effective charge repulsions. |
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%Can I increase the \sum size, not sure how... |
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\begin{equation} |
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E_{tot} = \sum_i F_i[\rho_{h,i}] + \frac{1}{2}\sum_i\sum_{j(\ne i)} \phi_{ij}(R_{ij}) |
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\end{equation} |
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\begin{equation} |
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\rho_{h,i} = \sum_{j (\ne i)} \rho_j^a(R_{ij}) |
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\end{equation} |
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The EAM functional forms are used to model the Au and Pt self-interactions in all of our simulations. |
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%CO |
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\subsection{CO} |
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Our CO model was obtained from work done by Karplus and Straub\cite{}. In their description of the biological importance of CO they developed an accurate quadrupolar model of CO which we make use of in this work. It has been suggested that the strong electrostatic repulsion that arises from this linear quadrupole may play an important role in the restructuring of metal surfaces to which CO is bound\cite{}. |
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The EAM, Finnis-Sinclair, and the Quantum Sutton-Chen (QSC) potentials |
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have all been widely used by the materials simulation community for |
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simulations of bulk and nanoparticle |
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properties,\cite{Chui:2003fk,Wang:2005qy,Medasani:2007uq} |
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melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr} |
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fracture,\cite{Shastry:1996qg,Shastry:1998dx} crack |
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propagation,\cite{BECQUART:1993rg} and alloying |
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dynamics.\cite{Shibata:2002hh} One of EAM's strengths |
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is its sensitivity to small changes in structure. This arises |
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because interactions |
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up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a} |
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Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88} |
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which is only parameterized up to the nearest-neighbor |
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interactions, EAM is a suitable choice for systems where |
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the bulk properties are of secondary importance to low-index |
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surface structures. Additionally, the similarity of EAM's functional |
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treatment of the embedding energy to standard density functional |
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theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
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\cite{Foiles86,PhysRevB.37.3924,Rifkin1992,mishin99:_inter,mishin01:cu,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
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|
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\subsection{Carbon Monoxide model} |
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Previous explanations for the surface rearrangements center on |
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the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} |
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We used a model first proposed by Karplus and Straub to study |
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the photodissociation of CO from myoglobin because it reproduces |
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the quadrupole moment well.\cite{Straub} The Straub and |
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Karplus model treats CO as a rigid three site molecule with a massless M |
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site at the molecular center of mass. The geometry and interaction |
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parameters are reproduced in Table~\ref{tab:CO}. The effective |
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dipole moment, calculated from the assigned charges, is still |
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small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
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to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
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mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
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%CO Table |
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\begin{table}[H] |
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\caption{$\sigma$, $\epsilon$ and charges for CO self-interactions\cite{}. Distances are in \AA~, energies are in kcal/mol, and charges are in $e$.} |
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\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
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$\epsilon$), and charges for the CO-CO |
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interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
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in kcal/mol, and charges are in atomic units.} |
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\centering |
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\begin{tabular}{| c | ccc |} |
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\begin{tabular}{| c | c | ccc |} |
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\hline |
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\multicolumn{4}{|c|}{\textbf{Self-Interactions}}\\ |
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& {\it z} & $\sigma$ & $\epsilon$ & q\\ |
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\hline |
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& $\sigma$ & $\epsilon$ & q\\ |
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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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\textbf{C} & 0.0262 & 3.83 & -0.75 \\ |
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\textbf{O} & 0.1591 & 3.12 & -0.85 \\ |
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\textbf{M} & - & - & 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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– |
%Cross |
| 98 |
– |
\subsection{Cross-Interactions} |
| 99 |
– |
To finish the forcefield, the cross-interactions between the metals and the CO needed to be parameterized. Previous attempts at parameterization have used two different functional forms to model these interactions\cite{}. A LJ model was fit for the Metal-Carbon interaction and a Morse potential was parameterized for the Metal-Oxygen interaction. The parameter sets chosen, as shown in Table 2, did a suitable job at reproducing experimental adsorption energies as shown in Table 3, but more importantly, they were able to capture the binding site preference. The Pt-CO parameters show a slight preference for the atop binding site which matches the experimental observations. |
| 262 |
|
|
| 263 |
+ |
\subsection{Cross-Interactions between the metals and carbon monoxide} |
| 264 |
|
|
| 265 |
+ |
Since the adsorption of CO onto a Pt surface has been the focus |
| 266 |
+ |
of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
| 267 |
+ |
and theoretical work |
| 268 |
+ |
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 269 |
+ |
there is a significant amount of data on adsorption energies for CO on |
| 270 |
+ |
clean metal surfaces. An earlier model by Korzeniewski {\it et |
| 271 |
+ |
al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
| 272 |
+ |
modified to ensure that the Pt-CO interaction favored the atop binding |
| 273 |
+ |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
| 274 |
+ |
The modified parameters yield binding energies that are slightly higher |
| 275 |
+ |
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 276 |
+ |
{\it et al}.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 277 |
+ |
Lennard-Jones interaction to mimic strong, but short-ranged, partial |
| 278 |
+ |
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 279 |
+ |
Pt-O interaction was modeled with a Morse potential with a large |
| 280 |
+ |
equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
| 281 |
+ |
over O as the surface-binding atom. In most geometries, the Pt-O parameterization contributes a weak |
| 282 |
+ |
repulsion which favors the atop site. The resulting potential-energy |
| 283 |
+ |
surface suitably recovers the calculated Pt-C separation length |
| 284 |
+ |
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 285 |
+ |
position.\cite{Deshlahra:2012, Hopster:1978} |
| 286 |
|
|
| 287 |
+ |
%where did you actually get the functionals for citation? |
| 288 |
+ |
%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
| 289 |
+ |
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 290 |
+ |
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 291 |
+ |
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 292 |
+ |
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
| 293 |
+ |
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 294 |
+ |
periodic supercell plane-wave basis approach, as implemented in the |
| 295 |
+ |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
| 296 |
+ |
described with the projector augmented-wave (PAW) |
| 297 |
+ |
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
| 298 |
+ |
included to an energy cutoff of 20 Ry. Electronic energies are |
| 299 |
+ |
computed with the PBE implementation of the generalized gradient |
| 300 |
+ |
approximation (GGA) for gold, carbon, and oxygen that was constructed |
| 301 |
+ |
by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
| 302 |
+ |
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
| 303 |
+ |
Au x 2 Au surface planes and separated from vertical images by six |
| 304 |
+ |
layers of vacuum space. The surface atoms were all allowed to relax |
| 305 |
+ |
before CO was added to the system. Electronic relaxations were |
| 306 |
+ |
performed until the energy difference between subsequent steps |
| 307 |
+ |
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
| 308 |
+ |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 309 |
+ |
zone.\cite{Monkhorst:1976} The relaxed gold slab was |
| 310 |
+ |
then used in numerous single point calculations with CO at various |
| 311 |
+ |
heights (and angles relative to the surface) to allow fitting of the |
| 312 |
+ |
empirical force field. |
| 313 |
|
|
| 314 |
< |
%\subsection{System} |
| 315 |
< |
%Once equilibration was reached, the systems were exposed to various sub-monolayer coverage of CO: $0, \frac{1}{10}, \frac{1}{4}, \frac{1}{3},\frac{1}{2}$. The CO was started many \AA~above the surface with random velocity and rotational velocity vectors sampling from a Gaussian distribution centered on the temperature of the equilibrated metal block. Full adsorption occurred over the period of approximately 10 ps for Pt, while the binding energy between Au and CO is smaller and led to an incomplete adsorption. The metal-metal interactions were treated using the Embedded Atom Method while the Pt-CO and Au-CO interactions were fit to experimental data and quantum calculations. The raised temperature helped shorten the length of the simulations by allowing the activation barrier of reconstruction to be more easily overcome. A few runs at lower temperatures showed the very beginnings of reconstructions, but their simulation lengths limited their usefulness. |
| 314 |
> |
%Hint at future work |
| 315 |
> |
The parameters employed for the metal-CO cross-interactions in this work |
| 316 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 317 |
> |
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 318 |
> |
and polarization are neglected in this model, although these effects could have |
| 319 |
> |
an effect on binding energies and binding site preferences. |
| 320 |
|
|
| 107 |
– |
|
| 321 |
|
%Table of Parameters |
| 322 |
|
%Pt Parameter Set 9 |
| 323 |
|
%Au Parameter Set 35 |
| 324 |
|
\begin{table}[H] |
| 325 |
< |
\caption{Best fit parameters for metal-adsorbate interactions. Distances are in \AA~and energies are in kcal/mol} |
| 325 |
> |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 326 |
> |
interactions are modeled with Lennard-Jones potentials. While the |
| 327 |
> |
metal-O interactions were fit to Morse |
| 328 |
> |
potentials. Distances are given in \AA~and energies in kcal/mol. } |
| 329 |
|
\centering |
| 330 |
|
\begin{tabular}{| c | cc | c | ccc |} |
| 331 |
|
\hline |
| 332 |
< |
\multicolumn{7}{| c |}{\textbf{Cross-Interactions} }\\ |
| 332 |
> |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ (\AA$^{-1}$) \\ |
| 333 |
|
\hline |
| 118 |
– |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\ |
| 119 |
– |
\hline |
| 334 |
|
\textbf{Pt-C} & 1.3 & 15 & \textbf{Pt-O} & 3.8 & 3.0 & 1 \\ |
| 335 |
|
\textbf{Au-C} & 1.9 & 6.5 & \textbf{Au-O} & 3.8 & 0.37 & 0.9\\ |
| 336 |
|
|
| 337 |
|
\hline |
| 338 |
|
\end{tabular} |
| 339 |
+ |
\label{tab:co_parameters} |
| 340 |
|
\end{table} |
| 341 |
|
|
| 342 |
|
%Table of energies |
| 343 |
|
\begin{table}[H] |
| 344 |
< |
\caption{Adsorption energies in eV} |
| 344 |
> |
\caption{Adsorption energies for a single CO at the atop site on M(111) at the atop site using the potentials |
| 345 |
> |
described in this work. All values are in eV.} |
| 346 |
|
\centering |
| 347 |
|
\begin{tabular}{| c | cc |} |
| 348 |
< |
\hline |
| 349 |
< |
& Calc. & Exp. \\ |
| 350 |
< |
\hline |
| 351 |
< |
\textbf{Pt-CO} & -1.9 & -1.4~\cite{Kelemen}-- -1.9~\cite{Yeo} \\ |
| 352 |
< |
\textbf{Au-CO} & -0.39 & -0.44~\cite{TPD_Gold_CO} \\ |
| 353 |
< |
\hline |
| 348 |
> |
\hline |
| 349 |
> |
& Calculated & Experimental \\ |
| 350 |
> |
\hline |
| 351 |
> |
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
| 352 |
> |
(Ref. \protect\cite{Kelemen:1979}) \\ |
| 353 |
> |
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
| 354 |
> |
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
| 355 |
> |
\hline |
| 356 |
|
\end{tabular} |
| 357 |
+ |
\label{tab:co_energies} |
| 358 |
|
\end{table} |
| 359 |
|
|
| 360 |
+ |
\subsection{Pt(557) and Au(557) metal interfaces} |
| 361 |
+ |
Our Pt system is an orthorhombic periodic box of dimensions |
| 362 |
+ |
54.482~x~50.046~x~120.88~\AA~while our Au system has |
| 363 |
+ |
dimensions of 57.4~x~51.9285~x~100~\AA. The metal slabs |
| 364 |
+ |
are 9 and 8 atoms deep respectively, corresponding to a slab |
| 365 |
+ |
thickness of $\sim$21~\AA~ for Pt and $\sim$19~\AA~for Au. |
| 366 |
+ |
The systems are arranged in a FCC crystal that have been cut |
| 367 |
+ |
along the (557) plane so that they are periodic in the {\it x} and |
| 368 |
+ |
{\it y} directions, and have been oriented to expose two aligned |
| 369 |
+ |
(557) cuts along the extended {\it z}-axis. Simulations of the |
| 370 |
+ |
bare metal interfaces at temperatures ranging from 300~K to |
| 371 |
+ |
1200~K were performed to confirm the relative |
| 372 |
+ |
stability of the surfaces without a CO overlayer. |
| 373 |
|
|
| 374 |
+ |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
| 375 |
+ |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
| 376 |
+ |
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 377 |
+ |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 378 |
+ |
respectively for 100 ps. The two surfaces were relatively stable at these |
| 379 |
+ |
temperatures when no CO was present, but experienced increased surface |
| 380 |
+ |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
| 381 |
+ |
that was initially placed in the vacuum region. Upon full adsorption, |
| 382 |
+ |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 383 |
+ |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
| 384 |
+ |
which introduces artifacts that are not relevant to (557) reconstruction. |
| 385 |
+ |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
| 386 |
+ |
the Au surfaces often had a significant CO population in the gas |
| 387 |
+ |
phase. These systems were allowed to reach thermal equilibrium (over |
| 388 |
+ |
5~ns) before being run in the microcanonical (NVE) ensemble for |
| 389 |
+ |
data collection. All of the systems examined had at least 40~ns in the |
| 390 |
+ |
data collection stage, although simulation times for some Pt of the |
| 391 |
+ |
systems exceeded 200~ns. Simulations were carried out using the open |
| 392 |
+ |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,openmd} |
| 393 |
|
|
| 394 |
|
|
| 395 |
|
|
| 396 |
|
|
| 397 |
< |
% Just results, leave discussion for discussion section |
| 397 |
> |
% RESULTS |
| 398 |
> |
% |
| 399 |
|
\section{Results} |
| 400 |
< |
\subsection{Diffusion} |
| 401 |
< |
While an ideal metallic surface is unlikely to experience much surface diffusion, high-index surfaces have large numbers of low-coordinated atoms which have a much easier time overcoming the energetic barriers limiting diffusion, leading to easier surface reconstructions. Surface movement was divided between the parallel ($\parallel$) and perpendicular ($\perp$) directions relative to the step edge. We were then able to calculate diffusion constants as a function of CO coverage. As can be seen in Table 4, the presence and amount of CO directly affects the diffusion constants of surface platinum atoms. The presence of two 50\% coverage systems is to show how the diffusion process is affected by time. The majority of the systems were run for approximately 50 ns while the half monolayer system been running continuously. The lowered diffusion constant at longer run times will be examined in-depth in the discussion section. |
| 400 |
> |
\subsection{Structural remodeling} |
| 401 |
> |
The bare metal surfaces experienced minor roughening of the |
| 402 |
> |
step-edge because of the elevated temperatures, but the (557) |
| 403 |
> |
face was stable throughout the simulations. The surface of both |
| 404 |
> |
systems, upon dosage of CO, began to undergo extensive remodeling |
| 405 |
> |
that was not observed in the bare systems. Reconstructions of |
| 406 |
> |
the Au systems were limited to breakup of the step-edges and |
| 407 |
> |
some step wandering. The lower coverage Pt systems experienced |
| 408 |
> |
similar restructuring but to a greater extent. The 50\% coverage |
| 409 |
> |
Pt system was unique among our simulations in that it formed |
| 410 |
> |
well-defined and stable double layers through step coalescence, |
| 411 |
> |
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
| 412 |
|
|
| 151 |
– |
%Table of Diffusion Constants |
| 152 |
– |
%Add gold?M |
| 153 |
– |
\begin{table}[H] |
| 154 |
– |
\caption{Platinum diffusion constants parallel and perpendicular to the 557 step edge. As the coverage increases, the diffusion constants parallel and perpendicular to the step edge both initially increase and then decrease slightly. There were two approaches of analysis. One looking at the surface atoms that had moved more than a prescribed amount over the run time and the other looking at all surface atoms. Units are \AA\textsuperscript{2}/ns} |
| 155 |
– |
\centering |
| 156 |
– |
\begin{tabular}{| c | ccc | ccc | c |} |
| 157 |
– |
\hline |
| 158 |
– |
\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\ |
| 159 |
– |
\hline |
| 160 |
– |
&\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\ |
| 161 |
– |
\hline |
| 162 |
– |
50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\ |
| 163 |
– |
50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46 \\ |
| 164 |
– |
33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46 \\ |
| 165 |
– |
25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46 \\ |
| 166 |
– |
5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46 \\ |
| 167 |
– |
0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56 \\ |
| 168 |
– |
\hline |
| 169 |
– |
50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68 & 925 & 25\\ |
| 170 |
– |
0\%-r & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\ |
| 171 |
– |
\hline |
| 172 |
– |
\end{tabular} |
| 173 |
– |
\end{table} |
| 413 |
|
|
| 414 |
+ |
\subsubsection{Step wandering} |
| 415 |
+ |
The 0\% coverage surfaces for both metals showed minimal |
| 416 |
+ |
step-wandering at their respective temperatures. As the CO |
| 417 |
+ |
coverage increased however, the mobility of the surface atoms, |
| 418 |
+ |
described through adatom diffusion and step-edge wandering, |
| 419 |
+ |
also increased. Except for the 50\% Pt system where step |
| 420 |
+ |
coalescence occurred, the step-edges in the other simulations |
| 421 |
+ |
preferred to keep nearly the same distance between steps as in |
| 422 |
+ |
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
| 423 |
+ |
Previous work by Williams {\it et al}.\cite{Williams:1991, Williams:1994} |
| 424 |
+ |
highlights the repulsion that exists between step-edges even |
| 425 |
+ |
when no direct interactions are present in the system. This |
| 426 |
+ |
repulsion is caused by an entropic barrier that arises from |
| 427 |
+ |
the fact that steps cannot cross over one another. This entropic |
| 428 |
+ |
repulsion does not completely define the interactions between |
| 429 |
+ |
steps, however, so it is possible to observe step coalescence |
| 430 |
+ |
on some surfaces.\cite{Williams:1991} The presence and |
| 431 |
+ |
concentration of adsorbates, as shown in this work, can |
| 432 |
+ |
affect step-step interactions, potentially leading to a new |
| 433 |
+ |
surface structure as the thermodynamic equilibrium. |
| 434 |
|
|
| 435 |
+ |
\subsubsection{Double layers} |
| 436 |
+ |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
| 437 |
+ |
undergoes two separate reconstructions upon CO adsorption. |
| 438 |
+ |
The first involves a doubling of the step height and plateau length. |
| 439 |
+ |
Similar behavior has been seen on a number of surfaces |
| 440 |
+ |
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 441 |
+ |
Of the two systems we examined, the Pt system showed a greater |
| 442 |
+ |
propensity for reconstruction |
| 443 |
+ |
because of the larger surface mobility and the greater extent of step wandering. |
| 444 |
+ |
The amount of reconstruction was strongly correlated to the amount of CO |
| 445 |
+ |
adsorbed upon the surface. This appears to be related to the |
| 446 |
+ |
effect that adsorbate coverage has on edge breakup and on the |
| 447 |
+ |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
| 448 |
+ |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
| 449 |
+ |
Over a longer time scale (150~ns) two more double layers formed |
| 450 |
+ |
on this surface. Although double layer formation did not occur |
| 451 |
+ |
in the other Pt systems, they exhibited more step-wandering and |
| 452 |
+ |
roughening compared to their Au counterparts. The |
| 453 |
+ |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 454 |
+ |
various times along the simulation showing the evolution of a double layer step-edge. |
| 455 |
|
|
| 456 |
+ |
The second reconstruction observed by |
| 457 |
+ |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
| 458 |
+ |
across the plateau between two step-edges. Neither metal, within |
| 459 |
+ |
the 40~ns time scale or the extended simulation time of 150~ns for |
| 460 |
+ |
the 50\% Pt system, experienced this reconstruction. |
| 461 |
+ |
|
| 462 |
+ |
%Evolution of surface |
| 463 |
+ |
\begin{figure}[H] |
| 464 |
+ |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} |
| 465 |
+ |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 466 |
+ |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 467 |
+ |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 468 |
+ |
doubling of the layers appears only after two adjacent step-edges |
| 469 |
+ |
touch. The circled spot in (b) nucleated the growth of the double |
| 470 |
+ |
step observed in the later configurations.} |
| 471 |
+ |
\label{fig:reconstruct} |
| 472 |
+ |
\end{figure} |
| 473 |
+ |
|
| 474 |
+ |
\subsection{Dynamics} |
| 475 |
+ |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
| 476 |
+ |
using STM, has been able to capture the coalescence of steps |
| 477 |
+ |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
| 478 |
+ |
provides an upper bound for the time required for the doubling |
| 479 |
+ |
to occur. By utilizing Molecular Dynamics we are able to probe |
| 480 |
+ |
the dynamics of these reconstructions at elevated temperatures |
| 481 |
+ |
and in this section we provide data on the timescales for transport |
| 482 |
+ |
properties, e.g. diffusion and layer formation time. |
| 483 |
+ |
|
| 484 |
+ |
|
| 485 |
+ |
\subsubsection{Transport of surface metal atoms} |
| 486 |
+ |
%forcedSystems/stepSeparation |
| 487 |
+ |
The wandering of a step-edge is a cooperative effect |
| 488 |
+ |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 489 |
+ |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 490 |
+ |
much surface diffusion because of the large energetic barrier that must |
| 491 |
+ |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 492 |
+ |
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 493 |
+ |
Single-atom break-away from a step-edge on a clean surface still imposes an |
| 494 |
+ |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 495 |
+ |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 496 |
+ |
The penalty lowers significantly when CO is present in sufficient quantities |
| 497 |
+ |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
| 498 |
+ |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 499 |
+ |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 500 |
+ |
able to explore the terrace before rejoining either their original step-edge or |
| 501 |
+ |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
| 502 |
+ |
to traverse to a separate terrace although the presence of CO can lower the |
| 503 |
+ |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 504 |
+ |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 505 |
+ |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 506 |
+ |
observation of the mobile metal atoms showed that they were typically in |
| 507 |
+ |
equilibrium with the step-edges. |
| 508 |
+ |
At times, their motion was concerted and two or more adatoms would be |
| 509 |
+ |
observed moving together across the surfaces. |
| 510 |
+ |
|
| 511 |
+ |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 512 |
+ |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
| 513 |
+ |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 514 |
+ |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 515 |
+ |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 516 |
+ |
local structures and in this work, the presence of single and double layer |
| 517 |
+ |
step-edges causes the diffusion parallel to the step-edges to be larger than |
| 518 |
+ |
the diffusion perpendicular to these edges. Parallel and perpendicular |
| 519 |
+ |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 520 |
+ |
|
| 521 |
+ |
%Diffusion graph |
| 522 |
+ |
\begin{figure}[H] |
| 523 |
+ |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1} |
| 524 |
+ |
\caption{Diffusion constants for mobile surface atoms along directions |
| 525 |
+ |
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 526 |
+ |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 527 |
+ |
surface coverage. Diffusion parallel to the step-edge is higher |
| 528 |
+ |
than that perpendicular to the edge because of the lower energy |
| 529 |
+ |
barrier associated with traversing along the edge as compared to |
| 530 |
+ |
completely breaking away. The two reported diffusion constants for |
| 531 |
+ |
the 50\% Pt system arise from different sample sets. The lower values |
| 532 |
+ |
correspond to the same 40~ns amount that all of the other systems were |
| 533 |
+ |
examined at, while the larger values correspond to a 20~ns period } |
| 534 |
+ |
\label{fig:diff} |
| 535 |
+ |
\end{figure} |
| 536 |
+ |
|
| 537 |
+ |
The weaker Au-CO interaction is evident in the weak CO-coverage |
| 538 |
+ |
dependance of Au diffusion. This weak interaction leads to lower |
| 539 |
+ |
observed coverages when compared to dosage amounts. This further |
| 540 |
+ |
limits the effect the CO can have on surface diffusion. The correlation |
| 541 |
+ |
between coverage and Pt diffusion rates shows a near linear relationship |
| 542 |
+ |
at the earliest times in the simulations. Following double layer formation, |
| 543 |
+ |
however, there is a precipitous drop in adatom diffusion. As the double |
| 544 |
+ |
layer forms, many atoms that had been tracked for mobility data have |
| 545 |
+ |
now been buried resulting in a smaller reported diffusion constant. A |
| 546 |
+ |
secondary effect of higher coverages is CO-CO cross interactions that |
| 547 |
+ |
lower the effective mobility of the Pt adatoms that are bound to each CO. |
| 548 |
+ |
This effect would become evident only at higher coverages. A detailed |
| 549 |
+ |
account of Pt adatom energetics follows in the Discussion. |
| 550 |
+ |
|
| 551 |
+ |
|
| 552 |
+ |
\subsubsection{Dynamics of double layer formation} |
| 553 |
+ |
The increased diffusion on Pt at the higher CO coverages is the primary |
| 554 |
+ |
contributor to double layer formation. However, this is not a complete |
| 555 |
+ |
explanation -- the 33\%~Pt system has higher diffusion constants, but |
| 556 |
+ |
did not show any signs of edge doubling in 40~ns. On the 50\%~Pt |
| 557 |
+ |
system, one double layer formed within the first 40~ns of simulation time, |
| 558 |
+ |
while two more were formed as the system was allowed to run for an |
| 559 |
+ |
additional 110~ns (150~ns total). This suggests that this reconstruction |
| 560 |
+ |
is a rapid process and that the previously mentioned upper bound is a |
| 561 |
+ |
very large overestimate.\cite{Williams:1991,Pearl} In this system the first |
| 562 |
+ |
appearance of a double layer appears at 19~ns into the simulation. |
| 563 |
+ |
Within 12~ns of this nucleation event, nearly half of the step has formed |
| 564 |
+ |
the double layer and by 86~ns the complete layer has flattened out. |
| 565 |
+ |
From the appearance of the first nucleation event to the first observed |
| 566 |
+ |
double layer, the process took $\sim$20~ns. Another $\sim$40~ns was |
| 567 |
+ |
necessary for the layer to completely straighten. The other two layers in |
| 568 |
+ |
this simulation formed over periods of 22~ns and 42~ns respectively. |
| 569 |
+ |
A possible explanation for this rapid reconstruction is the elevated |
| 570 |
+ |
temperatures under which our systems were simulated. The process |
| 571 |
+ |
would almost certainly take longer at lower temperatures. Additionally, |
| 572 |
+ |
our measured times for completion of the doubling after the appearance |
| 573 |
+ |
of a nucleation site are likely affected by our periodic boxes. A longer |
| 574 |
+ |
step-edge will likely take longer to ``zipper''. |
| 575 |
+ |
|
| 576 |
+ |
|
| 577 |
|
%Discussion |
| 578 |
|
\section{Discussion} |
| 579 |
< |
Comparing the results from simulation to those reported previously by Tao et al. the similarities in the platinum and CO system are quite strong. As shown in figure 1, the simulated platinum system under a CO atmosphere will restructure slightly by doubling the terrace heights. The restructuring appears to occur slowly, one to two platinum atoms at a time. Looking at individual snapshots, these adatoms tend to either rise on top of the plateau or break away from the step edge and then diffuse perpendicularly to the step direction until reaching another step edge. This combination of growth and decay of the step edges appears to be in somewhat of a state of dynamic equilibrium. However, once two previously separated edges meet as shown in figure 1.B, this point tends to act as a focus or growth point for the rest of the edge to meet up, akin to that of a zipper. From the handful of cases where a double layer was formed during the simulation. Measuring from the initial appearance of a growth point, the double layer tends to be fully formed within $\sim$~35 ns. |
| 579 |
> |
We have shown that a classical potential is able to model the initial |
| 580 |
> |
reconstruction of the Pt(557) surface upon CO adsorption, and have |
| 581 |
> |
reproduced the double layer structure observed by Tao {\it et |
| 582 |
> |
al}.\cite{Tao:2010}. Additionally, this reconstruction appears to be |
| 583 |
> |
rapid -- occurring within 100 ns of the initial exposure to CO. Here |
| 584 |
> |
we discuss the features of the classical potential that are |
| 585 |
> |
contributing to the stability and speed of the Pt(557) reconstruction. |
| 586 |
|
|
| 587 |
|
\subsection{Diffusion} |
| 588 |
< |
As shown in the results section, the diffusion parallel to the step edge tends to be much faster than that perpendicular to the step edge. Additionally, the coverage of CO appears to play a slight role in relative rates of diffusion, as shown in Table 4. Thus, the bottleneck of the double layer formation appears to be the initial formation of this growth point, which seems to be somewhat of a stochastic event. Once it appears, parallel diffusion, along the now slightly angled step edge, will allow for a faster formation of the double layer than if the entire process were dependent on only perpendicular diffusion across the plateaus. Thus, the larger $D_{\perp}$, the more likely a growth point is to be formed. One driving force behind this reconstruction appears to be the lowering of surface energy that occurs by doubling the terrace widths. (I'm not really proving this... I have the surface flatness to show it, but surface energy?) |
| 589 |
< |
\\ |
| 590 |
< |
\\ |
| 591 |
< |
%Evolution of surface |
| 588 |
> |
The perpendicular diffusion constant appears to be the most important |
| 589 |
> |
indicator of double layer formation. As highlighted in Figure |
| 590 |
> |
\ref{fig:reconstruct}, the formation of the double layer did not begin |
| 591 |
> |
until a nucleation site appeared. Williams {\it et |
| 592 |
> |
al}.\cite{Williams:1991,Williams:1994} cite an effective edge-edge |
| 593 |
> |
repulsion arising from the inability of edge crossing. This repulsion |
| 594 |
> |
must be overcome to allow step coalescence. A larger |
| 595 |
> |
$\textbf{D}_\perp$ value implies more step-wandering and a larger |
| 596 |
> |
chance for the stochastic meeting of two edges to create a nucleation |
| 597 |
> |
point. Diffusion parallel to the step-edge can help ``zipper'' up a |
| 598 |
> |
nascent double layer. This helps explain the rapid time scale for |
| 599 |
> |
double layer completion after the appearance of a nucleation site, while |
| 600 |
> |
the initial appearance of the nucleation site was unpredictable. |
| 601 |
> |
|
| 602 |
> |
\subsection{Mechanism for restructuring} |
| 603 |
> |
Since the Au surface showed no large scale restructuring in any of our |
| 604 |
> |
simulations, our discussion will focus on the 50\% Pt-CO system which |
| 605 |
> |
did exhibit doubling. A number of possible mechanisms exist to explain |
| 606 |
> |
the role of adsorbed CO in restructuring the Pt surface. Quadrupolar |
| 607 |
> |
repulsion between adjacent CO molecules adsorbed on the surface is one |
| 608 |
> |
possibility. However, the quadrupole-quadrupole interaction is |
| 609 |
> |
short-ranged and is attractive for some orientations. If the CO |
| 610 |
> |
molecules are ``locked'' in a vertical orientation, through atop |
| 611 |
> |
adsorption for example, this explanation would gain credence. The |
| 612 |
> |
calculated energetic repulsion between two CO molecules located a |
| 613 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both |
| 614 |
> |
in a vertical orientation, is 8.62 kcal/mol. Moving the CO to the |
| 615 |
> |
second nearest-neighbor distance of 4.8~\AA~drops the repulsion to |
| 616 |
> |
nearly 0. Allowing the CO to rotate away from a purely vertical |
| 617 |
> |
orientation also lowers the repulsion. When the carbons are locked at |
| 618 |
> |
a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the |
| 619 |
> |
angle between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
| 620 |
> |
barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 621 |
> |
repulsion between adjacent CO molecules bound to Pt could increase the |
| 622 |
> |
surface diffusion. However, the residence time of CO on Pt suggests |
| 623 |
> |
that the CO molecules are extremely mobile, with diffusion constants 40 |
| 624 |
> |
to 2500 times larger than surface Pt atoms. This mobility suggests |
| 625 |
> |
that the CO molecules jump between different Pt atoms throughout the |
| 626 |
> |
simulation, but can stay bound for significant periods of time. |
| 627 |
> |
|
| 628 |
> |
A different interpretation of the above mechanism which takes the |
| 629 |
> |
large mobility of the CO into account, would be in the destabilization |
| 630 |
> |
of Pt-Pt interactions due to bound CO. Destabilizing Pt-Pt bonds at |
| 631 |
> |
the edges could lead to increased step-edge breakup and diffusion. On |
| 632 |
> |
the bare Pt(557) surface the barrier to completely detach an edge atom |
| 633 |
> |
is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
| 634 |
> |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain |
| 635 |
> |
configurations, cases (e), (g), and (h), the barrier can be lowered to |
| 636 |
> |
$\sim$23~kcal/mol by the presence of bound CO molecules. In these |
| 637 |
> |
instances, it becomes energetically favorable to roughen the edge by |
| 638 |
> |
introducing a small separation of 0.5 to 1.0~\AA. This roughening |
| 639 |
> |
becomes immediately obvious in simulations with significant CO |
| 640 |
> |
populations. The roughening is present to a lesser extent on surfaces |
| 641 |
> |
with lower CO coverage (and even on the bare surfaces), although in |
| 642 |
> |
these cases it is likely due to random fluctuations that squeeze out |
| 643 |
> |
step-edge atoms. Step-edge breakup by continuous single-atom |
| 644 |
> |
translations (as suggested by these energy curves) is probably a |
| 645 |
> |
worst-case scenario. Multistep mechanisms in which an adatom moves |
| 646 |
> |
laterally on the surface after being ejected would be more |
| 647 |
> |
energetically favorable. This would leave the adatom alongside the |
| 648 |
> |
ledge, providing it with 5 nearest neighbors. While fewer than the 7 |
| 649 |
> |
neighbors it had as part of the step-edge, it keeps more Pt neighbors |
| 650 |
> |
than the 3 an isolated adatom would have on the terrace. In this |
| 651 |
> |
proposed mechanism, the CO quadrupolar repulsion still plays a role in |
| 652 |
> |
the initial roughening of the step-edge, but not in any long-term |
| 653 |
> |
bonds with individual Pt atoms. Higher CO coverages create more |
| 654 |
> |
opportunities for the crowded CO configurations shown in Figure |
| 655 |
> |
\ref{fig:SketchGraphic}, and this is likely to cause an increased |
| 656 |
> |
propensity for step-edge breakup. |
| 657 |
> |
|
| 658 |
> |
%Sketch graphic of different configurations |
| 659 |
|
\begin{figure}[H] |
| 660 |
< |
\includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 661 |
< |
\caption{Four snapshots at various times a) 258 ps b) 19 ns c) 31.2 ns d) 86.1 ns. Slight disruption of the surface occurs fairly quickly. However, the doubling of the layers seems to be very dependent on the initial linking of two separate step edges. The focal point in b, appears to be a growth spot for the rest of the double layer.} |
| 660 |
> |
\includegraphics[width=\linewidth]{COpaths} |
| 661 |
> |
\caption{Configurations used to investigate the mechanism of step-edge |
| 662 |
> |
breakup on Pt(557). In each case, the central (starred) atom is |
| 663 |
> |
pulled directly across the surface away from the step edge. The Pt |
| 664 |
> |
atoms on the upper terrace are colored dark grey, while those on the |
| 665 |
> |
lower terrace are in white. In each of these configurations, some |
| 666 |
> |
number of the atoms (highlighted in blue) had a CO molecule bound in |
| 667 |
> |
a vertical atop position. The energies of these configurations as a |
| 668 |
> |
function of central atom displacement are displayed in Figure |
| 669 |
> |
\ref{fig:SketchEnergies}.} |
| 670 |
> |
\label{fig:SketchGraphic} |
| 671 |
|
\end{figure} |
| 672 |
|
|
| 673 |
+ |
%energy graph corresponding to sketch graphic |
| 674 |
+ |
\begin{figure}[H] |
| 675 |
+ |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison} |
| 676 |
+ |
\caption{Energies for displacing a single edge atom perpendicular to |
| 677 |
+ |
the step edge as a function of atomic displacement. Each of the |
| 678 |
+ |
energy curves corresponds to one of the labeled configurations in |
| 679 |
+ |
Figure \ref{fig:SketchGraphic}, and are referenced to the |
| 680 |
+ |
unperturbed step-edge. Certain arrangements of bound CO (notably |
| 681 |
+ |
configurations g and h) can lower the energetic barrier for creating |
| 682 |
+ |
an adatom relative to the bare surface (configuration a).} |
| 683 |
+ |
\label{fig:SketchEnergies} |
| 684 |
+ |
\end{figure} |
| 685 |
|
|
| 686 |
+ |
While configurations of CO on the surface are able to increase |
| 687 |
+ |
diffusion and the likelihood of edge wandering, this does not provide |
| 688 |
+ |
a complete explanation for the formation of double layers. If adatoms |
| 689 |
+ |
were constrained to their original terraces then doubling could not |
| 690 |
+ |
occur. A mechanism for vertical displacement of adatoms at the |
| 691 |
+ |
step-edge is required to explain the doubling. |
| 692 |
|
|
| 693 |
+ |
We have discovered one possible mechanism for a CO-mediated vertical |
| 694 |
+ |
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} |
| 695 |
+ |
shows four points along a reaction coordinate in which a CO-bound |
| 696 |
+ |
adatom along the step-edge ``burrows'' into the edge and displaces the |
| 697 |
+ |
original edge atom onto the higher terrace. A number of events similar |
| 698 |
+ |
to this mechanism were observed during the simulations. We predict an |
| 699 |
+ |
energetic barrier of 20~kcal/mol for this process (in which the |
| 700 |
+ |
displaced edge atom follows a curvilinear path into an adjacent 3-fold |
| 701 |
+ |
hollow site). The barrier heights we obtain for this reaction |
| 702 |
+ |
coordinate are approximate because the exact path is unknown, but the |
| 703 |
+ |
calculated energy barriers would be easily accessible at operating |
| 704 |
+ |
conditions. Additionally, this mechanism is exothermic, with a final |
| 705 |
+ |
energy 15~kcal/mol below the original $\lambda = 0$ configuration. |
| 706 |
+ |
When CO is not present and this reaction coordinate is followed, the |
| 707 |
+ |
process is endothermic by 3~kcal/mol. The difference in the relative |
| 708 |
+ |
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present |
| 709 |
+ |
provides strong support for CO-mediated Pt-Pt interactions giving rise |
| 710 |
+ |
to the doubling reconstruction. |
| 711 |
|
|
| 712 |
+ |
%lambda progression of Pt -> shoving its way into the step |
| 713 |
+ |
\begin{figure}[H] |
| 714 |
+ |
\includegraphics[width=\linewidth]{EPS_rxnCoord} |
| 715 |
+ |
\caption{Points along a possible reaction coordinate for CO-mediated |
| 716 |
+ |
edge doubling. Here, a CO-bound adatom burrows into an established |
| 717 |
+ |
step edge and displaces an edge atom onto the upper terrace along a |
| 718 |
+ |
curvilinear path. The approximate barrier for the process is |
| 719 |
+ |
20~kcal/mol, and the complete process is exothermic by 15~kcal/mol |
| 720 |
+ |
in the presence of CO, but is endothermic by 3~kcal/mol without.} |
| 721 |
+ |
\label{fig:lambda} |
| 722 |
+ |
\end{figure} |
| 723 |
+ |
|
| 724 |
+ |
The mechanism for doubling on the Pt(557) surface appears to require |
| 725 |
+ |
the cooperation of at least two distinct processes. For complete |
| 726 |
+ |
doubling of a layer to occur there must be a breakup of one |
| 727 |
+ |
terrace. These atoms must then ``disappear'' from that terrace, either |
| 728 |
+ |
by travelling to the terraces above of below their original levels. |
| 729 |
+ |
The presence of CO helps explain mechanisms for both of these |
| 730 |
+ |
situations. There must be sufficient breakage of the step-edge to |
| 731 |
+ |
increase the concentration of adatoms on the surface and these adatoms |
| 732 |
+ |
must then undergo the burrowing highlighted above (or a comparable |
| 733 |
+ |
mechanism) to create the double layer. With sufficient time, these |
| 734 |
+ |
mechanisms working in concert lead to the formation of a double layer. |
| 735 |
+ |
|
| 736 |
+ |
\subsection{CO Removal and double layer stability} |
| 737 |
+ |
Once a double layer had formed on the 50\%~Pt system, it remained for |
| 738 |
+ |
the rest of the simulation time with minimal movement. Random |
| 739 |
+ |
fluctuations that involved small clusters or divots were observed, but |
| 740 |
+ |
these features typically healed within a few nanoseconds. Within our |
| 741 |
+ |
simulations, the formation of the double layer appeared to be |
| 742 |
+ |
irreversible and a double layer was never observed to split back into |
| 743 |
+ |
two single layer step-edges while CO was present. |
| 744 |
+ |
|
| 745 |
+ |
To further gauge the effect CO has on this surface, additional |
| 746 |
+ |
simulations were run starting from a late configuration of the 50\%~Pt |
| 747 |
+ |
system that had already formed double layers. These simulations then |
| 748 |
+ |
had their CO forcibly removed. The double layer broke apart rapidly |
| 749 |
+ |
in these simulations, showing a well-defined edge-splitting after |
| 750 |
+ |
100~ps. Configurations of this system are shown in Figure |
| 751 |
+ |
\ref{fig:breaking}. The coloring of the top and bottom layers helps to |
| 752 |
+ |
exhibit how much mixing the edges experience as they split. These |
| 753 |
+ |
systems were only examined for 10~ns, and within that time despite the |
| 754 |
+ |
initial rapid splitting, the edges only moved another few |
| 755 |
+ |
\AA~apart. It is possible that with longer simulation times, the (557) |
| 756 |
+ |
surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could |
| 757 |
+ |
also be recovered. |
| 758 |
+ |
|
| 759 |
+ |
%breaking of the double layer upon removal of CO |
| 760 |
+ |
\begin{figure}[H] |
| 761 |
+ |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} |
| 762 |
+ |
\caption{Dynamics of an established (111) double step after removal of |
| 763 |
+ |
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal |
| 764 |
+ |
of CO. The presence of the CO helped maintain the stability of the |
| 765 |
+ |
double step. Nearly immediately after the CO is removed, the step |
| 766 |
+ |
edge reforms in a (100) configuration, which is also the step type |
| 767 |
+ |
seen on clean (557) surfaces. The step separation involves |
| 768 |
+ |
significant mixing of the lower and upper atoms at the edge.} |
| 769 |
+ |
\label{fig:breaking} |
| 770 |
+ |
\end{figure} |
| 771 |
+ |
|
| 772 |
+ |
|
| 773 |
|
%Peaks! |
| 774 |
< |
\includegraphics[scale=0.25]{doublePeaks_noCO.png} |
| 775 |
< |
\section{Conclusion} |
| 774 |
> |
%\begin{figure}[H] |
| 775 |
> |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 776 |
> |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 777 |
> |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 778 |
> |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 779 |
> |
%\label{fig:peaks} |
| 780 |
> |
%\end{figure} |
| 781 |
|
|
| 782 |
|
|
| 783 |
+ |
%Don't think I need this |
| 784 |
+ |
%clean surface... |
| 785 |
+ |
%\begin{figure}[H] |
| 786 |
+ |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF} |
| 787 |
+ |
%\caption{} |
| 788 |
|
|
| 789 |
+ |
%\end{figure} |
| 790 |
+ |
%\label{fig:clean} |
| 791 |
|
|
| 792 |
|
|
| 793 |
+ |
\section{Conclusion} |
| 794 |
+ |
The strength and directionality of the Pt-CO binding interaction, as |
| 795 |
+ |
well as the large quadrupolar repulsion between atop-bound CO |
| 796 |
+ |
molecules, help to explain the observed increase in surface mobility |
| 797 |
+ |
of Pt(557) and the resultant reconstruction into a double-layer |
| 798 |
+ |
configuration at the highest simulated CO-coverages. The weaker Au-CO |
| 799 |
+ |
interaction results in significantly lower adataom diffusion |
| 800 |
+ |
constants, less step-wandering, and a lack of the double layer |
| 801 |
+ |
reconstruction on the Au(557) surface. |
| 802 |
|
|
| 803 |
+ |
An in-depth examination of the energetics shows the important role CO |
| 804 |
+ |
plays in increasing step-breakup and in facilitating edge traversal |
| 805 |
+ |
which are both necessary for double layer formation. |
| 806 |
|
|
| 807 |
+ |
%Things I am not ready to remove yet |
| 808 |
|
|
| 809 |
+ |
%Table of Diffusion Constants |
| 810 |
+ |
%Add gold?M |
| 811 |
+ |
% \begin{table}[H] |
| 812 |
+ |
% \caption{} |
| 813 |
+ |
% \centering |
| 814 |
+ |
% \begin{tabular}{| c | cc | cc | } |
| 815 |
+ |
% \hline |
| 816 |
+ |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 817 |
+ |
% \hline |
| 818 |
+ |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 819 |
+ |
% \hline |
| 820 |
+ |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 821 |
+ |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 822 |
+ |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 823 |
+ |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 824 |
+ |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
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+ |
% \hline |
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% \end{tabular} |
| 827 |
+ |
% \end{table} |
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|
|
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\begin{acknowledgement} |
| 830 |
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We gratefully acknowledge conversations with Dr. William |
| 831 |
+ |
F. Schneider and Dr. Feng Tao. Support for this project was |
| 832 |
+ |
provided by the National Science Foundation under grant CHE-0848243 |
| 833 |
+ |
and by the Center for Sustainable Energy at Notre Dame |
| 834 |
+ |
(cSEND). Computational time was provided by the Center for Research |
| 835 |
+ |
Computing (CRC) at the University of Notre Dame. |
| 836 |
+ |
\end{acknowledgement} |
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\newpage |
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\bibliography{firstTryBibliography} |
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%\end{doublespace} |
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\begin{tocentry} |
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%\includegraphics[height=3.5cm]{timelapse} |
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\includegraphics[height=3.5cm]{TOC_doubleLayer.pdf} |
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\end{tocentry} |
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< |
\end{document} |
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> |
\end{document} |
