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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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\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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\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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\end{abstract} |
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\doublespacing |
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\newpage |
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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: 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 likely 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: high pressures, temperatures, etc. are able to cause reconstructions of the 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 giving a clearer picture of what processes are occurring on metal surfaces when exposed to \emph{in situ} conditions. But all of these techniques still have difficulties, especially in observing what is occurring on the surfaces 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 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 absorption energies, preferred absorption 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 will undergo 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 |
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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 seen as less |
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likely to undergo this kind of reconstruction. However, Peters et al.\cite{Peters:2000} |
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and Piccolo et al.\cite{Piccolo:2004} have both observed CO-induced |
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reconstruction of a Au(111) surface. Peters 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 being greatly |
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affected by this relaxation. Piccolo 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 nearly 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 large number of low-coordination atoms along the step edges provide a suitable model for industrial catalysts which tend to have a prevalence of lower CN, i.e. more reactive, sites. Drawing from experimental conclusions, the reconstructions seen for the Pt 557 surface involve doubling of the step height and the formation of triangular motifs along the steps \cite{doi:10.1126/science.1182122}. To properly observe these changes, our system size need to be greater than the periodic phenomena we are examining. The large size and the long time scales needed precluded us from using expensive quantum approaches. Thus, a forcefield describing the Metal-Metal, CO-CO, and CO-Metal interactions was parameterized. |
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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. This description of the embedding energy allows this method to more accurately treat surfaces, alloys, and other non-bulk systems. 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 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$^6$ atoms) and respond slowly to perturbations, {\it ab initio} |
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molecular dynamics |
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(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
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methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
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mechanical potential energy surfaces remain out of reach. |
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Additionally, the ``bonds'' between metal atoms at a surface are |
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typically not well represented in terms of classical pairwise |
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interactions in the same way that bonds in a molecular material are, |
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nor are they captured by simple non-directional interactions like the |
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Coulomb potential. For this work, we have used classical molecular |
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dynamics with potential energy surfaces that are specifically tuned |
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for transition metals. In particular, we used the EAM potential for |
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Au-Au and Pt-Pt interactions\cite{EAM}. 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 et al. is among the |
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fastest of these density functional approaches.\cite{Ercolessi88} In |
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all of these models, atoms are conceptualized as a positively charged |
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core with a radially-decaying valence electron distribution. To |
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calculate the energy for embedding the core at a particular location, |
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the electron density due to the valence electrons at all of the other |
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atomic sites is computed at atom $i$'s location, |
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\begin{equation*} |
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\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}) |
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\end{equation*} |
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Here, $\rho_j(r_{ij})$ is the function that describes the distance |
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dependence of the valence electron distribution of atom $j$. The |
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contribution to the potential that comes from placing atom $i$ at that |
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location is then |
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\begin{equation*} |
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V_i = F[ \bar{\rho}_i ] + \sum_{j \neq i} \phi_{ij}(r_{ij}) |
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\end{equation*} |
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where $F[ \bar{\rho}_i ]$ is an energy embedding functional, and |
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$\phi_{ij}(r_{ij})$ is 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 |
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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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from the original parameterization, where the interactions |
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up to the third nearest neighbor were taken into account.\cite{Voter95a} |
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Comparing that to the glue model of Ercolessi 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 EAMs 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 |
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\subsection{Cross-Interactions} |
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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. |
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|
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\subsection{Cross-Interactions between the metals and carbon monoxide} |
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|
| 264 |
+ |
Since the adsorption of CO onto a Pt surface has been the focus |
| 265 |
+ |
of much experimental \cite{Yeo, Hopster:1978, Ertl:1977, Kelemen:1979} |
| 266 |
+ |
and theoretical work |
| 267 |
+ |
\cite{Beurden:2002ys,Pons:1986,Deshlahra:2009,Feibelman:2001,Mason:2004} |
| 268 |
+ |
there is a significant amount of data on adsorption energies for CO on |
| 269 |
+ |
clean metal surfaces. An earlier model by Korzeniewski {\it et |
| 270 |
+ |
al.}\cite{Pons:1986} served as a starting point for our fits. The parameters were |
| 271 |
+ |
modified to ensure that the Pt-CO interaction favored the atop binding |
| 272 |
+ |
position on Pt(111). These parameters are reproduced in Table~\ref{tab:co_parameters}. |
| 273 |
+ |
The modified parameters yield binding energies that are slightly higher |
| 274 |
+ |
than the experimentally-reported values as shown in Table~\ref{tab:co_energies}. Following Korzeniewski |
| 275 |
+ |
et al.,\cite{Pons:1986} the Pt-C interaction was fit to a deep |
| 276 |
+ |
Lennard-Jones interaction to mimic strong, but short-ranged partial |
| 277 |
+ |
binding between the Pt $d$ orbitals and the $\pi^*$ orbital on CO. The |
| 278 |
+ |
Pt-O interaction was modeled with a Morse potential with a large |
| 279 |
+ |
equilibrium distance, ($r_o$). These choices ensure that the C is preferred |
| 280 |
+ |
over O as the surface-binding atom. In most cases, the Pt-O parameterization contributes a weak |
| 281 |
+ |
repulsion which favors the atop site. The resulting potential-energy |
| 282 |
+ |
surface suitably recovers the calculated Pt-C separation length |
| 283 |
+ |
(1.6~\AA)\cite{Beurden:2002ys} and affinity for the atop binding |
| 284 |
+ |
position.\cite{Deshlahra:2012, Hopster:1978} |
| 285 |
|
|
| 286 |
+ |
%where did you actually get the functionals for citation? |
| 287 |
+ |
%scf calculations, so initial relaxation was of the four layers, but two layers weren't kept fixed, I don't think |
| 288 |
+ |
%same cutoff for slab and slab + CO ? seems low, although feibelmen had values around there... |
| 289 |
+ |
The Au-C and Au-O cross-interactions were also fit using Lennard-Jones and |
| 290 |
+ |
Morse potentials, respectively, to reproduce Au-CO binding energies. |
| 291 |
+ |
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
| 292 |
+ |
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 293 |
+ |
periodic supercell plane-wave basis approach, as implemented in the |
| 294 |
+ |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
| 295 |
+ |
described with the projector augmented-wave (PAW) |
| 296 |
+ |
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
| 297 |
+ |
included to an energy cutoff of 20 Ry. Electronic energies are |
| 298 |
+ |
computed with the PBE implementation of the generalized gradient |
| 299 |
+ |
approximation (GGA) for gold, carbon, and oxygen that was constructed |
| 300 |
+ |
by Rappe, Rabe, Kaxiras, and Joannopoulos.\cite{Perdew_GGA,RRKJ_PP} |
| 301 |
+ |
In testing the Au-CO interaction, Au(111) supercells were constructed of four layers of 4 |
| 302 |
+ |
Au x 2 Au surface planes and separated from vertical images by six |
| 303 |
+ |
layers of vacuum space. The surface atoms were all allowed to relax |
| 304 |
+ |
before CO was added to the system. Electronic relaxations were |
| 305 |
+ |
performed until the energy difference between subsequent steps |
| 306 |
+ |
was less than $10^{-8}$ Ry. Nonspin-polarized supercell calculations |
| 307 |
+ |
were performed with a 4~x~4~x~4 Monkhorst-Pack {\bf k}-point sampling of the first Brillouin |
| 308 |
+ |
zone.\cite{Monkhorst:1976} The relaxed gold slab was |
| 309 |
+ |
then used in numerous single point calculations with CO at various |
| 310 |
+ |
heights (and angles relative to the surface) to allow fitting of the |
| 311 |
+ |
empirical force field. |
| 312 |
|
|
| 313 |
< |
%\subsection{System} |
| 314 |
< |
%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. |
| 313 |
> |
%Hint at future work |
| 314 |
> |
The parameters employed for the metal-CO cross-interactions in this work |
| 315 |
> |
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 316 |
> |
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 317 |
> |
and polarization are neglected in this model, although these effects are likely to |
| 318 |
> |
affect binding energies and binding site preferences, and will be addressed in |
| 319 |
> |
future work. |
| 320 |
|
|
| 104 |
– |
|
| 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 |
| 115 |
– |
& $\sigma$ & $\epsilon$ & & $r$ & $D$ & $\gamma$ \\ |
| 116 |
– |
\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{Absorption 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. |
| 364 |
+ |
The systems are arranged in a FCC crystal that have been cut |
| 365 |
+ |
along the (557) plane so that they are periodic in the {\it x} and |
| 366 |
+ |
{\it y} directions, and have been oriented to expose two aligned |
| 367 |
+ |
(557) cuts along the extended {\it z}-axis. Simulations of the |
| 368 |
+ |
bare metal interfaces at temperatures ranging from 300~K to |
| 369 |
+ |
1200~K were performed to confirm the relative |
| 370 |
+ |
stability of the surfaces without a CO overlayer. |
| 371 |
|
|
| 372 |
+ |
The different bulk melting temperatures (1345~$\pm$~10~K for Au\cite{Au:melting} |
| 373 |
+ |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
| 374 |
+ |
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 375 |
+ |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 376 |
+ |
respectively for 100 ps. The two surfaces were relatively stable at these |
| 377 |
+ |
temperatures when no CO was present, but experienced increased surface |
| 378 |
+ |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
| 379 |
+ |
that was initially placed in the vacuum region. Upon full adsorption, |
| 380 |
+ |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 381 |
+ |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
| 382 |
+ |
which introduces artifacts that are not relevant to (557) reconstruction. |
| 383 |
+ |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
| 384 |
+ |
the Au surfaces often had a significant CO population in the gas |
| 385 |
+ |
phase. These systems were allowed to reach thermal equilibrium (over |
| 386 |
+ |
5~ns) before being run in the microcanonical (NVE) ensemble for |
| 387 |
+ |
data collection. All of the systems examined had at least 40~ns in the |
| 388 |
+ |
data collection stage, although simulation times for some Pt of the |
| 389 |
+ |
systems exceeded 200~ns. Simulations were carried out using the open |
| 390 |
+ |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE} |
| 391 |
|
|
| 392 |
|
|
| 393 |
|
|
| 394 |
|
|
| 395 |
< |
% Just results, leave discussion for discussion section |
| 395 |
> |
% RESULTS |
| 396 |
> |
% |
| 397 |
|
\section{Results} |
| 398 |
< |
\subsection{Diffusion} |
| 399 |
< |
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. |
| 398 |
> |
\subsection{Structural remodeling} |
| 399 |
> |
The surfaces of both systems, upon dosage of CO, began |
| 400 |
> |
to undergo extensive remodeling that was not observed in the bare |
| 401 |
> |
systems. The bare metal surfaces |
| 402 |
> |
experienced minor roughening of the step-edge because |
| 403 |
> |
of the elevated temperatures, but the |
| 404 |
> |
(557) lattice was well-maintained throughout the simulation |
| 405 |
> |
time. The Au systems were limited to greater amounts of |
| 406 |
> |
roughening, i.e. breakup of the step-edge, and some step |
| 407 |
> |
wandering. The lower coverage Pt systems experienced |
| 408 |
> |
similar restructuring but to a greater extent when |
| 409 |
> |
compared to the Au systems. The 50\% coverage |
| 410 |
> |
Pt system was unique among our simulations in that it |
| 411 |
> |
formed numerous double layers through step coalescence, |
| 412 |
> |
similar to results reported by Tao et al.\cite{Tao:2010} |
| 413 |
> |
|
| 414 |
> |
|
| 415 |
> |
\subsubsection{Step wandering} |
| 416 |
> |
The 0\% coverage surfaces for both metals showed minimal |
| 417 |
> |
movement at their respective run temperatures. As the CO |
| 418 |
> |
coverage increased however, the mobility of the surface, |
| 419 |
> |
described through adatom diffusion and step-edge wandering, |
| 420 |
> |
also increased. Except for the 50\% Pt system, the step-edges |
| 421 |
> |
did not coalesce in any of the other simulations, instead |
| 422 |
> |
preferring to keep nearly the same distance between steps |
| 423 |
> |
as in the original (557) lattice, $\sim$13\AA for Pt and $\sim$14\AA for Au. |
| 424 |
> |
Previous work by Williams et al.\cite{Williams:1991, Williams:1994} |
| 425 |
> |
highlights the repulsion that exists between step-edges even |
| 426 |
> |
when no direct interactions are present in the system. This |
| 427 |
> |
repulsion arises because step-edge crossing is not allowed |
| 428 |
> |
which constrains the entropy. This entropic repulsion does |
| 429 |
> |
not completely define the interactions between steps, which |
| 430 |
> |
is why some surfaces will undergo step coalescence, where |
| 431 |
> |
additional attractive interactions can overcome the repulsion.\cite{Williams:1991} |
| 432 |
> |
The presence and concentration of adsorbates, as shown in |
| 433 |
> |
this work, can affect these step interactions, potentially leading |
| 434 |
> |
to a new surface structure as the thermodynamic minimum. |
| 435 |
|
|
| 436 |
< |
%Table of Diffusion Constants |
| 437 |
< |
%Add gold?M |
| 438 |
< |
\begin{table}[H] |
| 439 |
< |
\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} |
| 440 |
< |
\centering |
| 441 |
< |
\begin{tabular}{| c | ccc | ccc | c |} |
| 442 |
< |
\hline |
| 443 |
< |
\textbf{System Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & \textbf{Atoms} & \textbf{Time (ns)}\\ |
| 444 |
< |
\hline |
| 445 |
< |
&\multicolumn{3}{c|}{\textbf{Mobile}}&\multicolumn{3}{c|}{\textbf{Surface Atoms}} & \\ |
| 446 |
< |
\hline |
| 447 |
< |
50\% & 3.74 & 0.89 & 497 & 2.05 & 0.49 & 912 & 116 \\ |
| 448 |
< |
50\% & 5.81 & 1.59 & 365 & 2.41 & 0.68 & 912 & 46 \\ |
| 449 |
< |
33\% & 6.73 & 2.47 & 332 & 2.51 & 0.93 & 912 & 46 \\ |
| 450 |
< |
25\% & 5.38 & 2.04 & 361 & 2.18 & 0.84 & 912 & 46 \\ |
| 451 |
< |
5\% & 5.54 & 0.63 & 230 & 1.44 & 0.19 & 912 & 46 \\ |
| 452 |
< |
0\% & 3.53 & 0.61 & 282 & 1.11 & 0.22 & 912 & 56 \\ |
| 453 |
< |
\hline |
| 454 |
< |
50\%-r & 6.91 & 2.00 & 198 & 2.23 & 0.68 & 925 & 25\\ |
| 455 |
< |
0\%-r & 4.73 & 0.27 & 128 & 0.72 & 0.05 & 925 & 43\\ |
| 456 |
< |
\hline |
| 169 |
< |
\end{tabular} |
| 170 |
< |
\end{table} |
| 436 |
> |
\subsubsection{Double layers} |
| 437 |
> |
Tao et al.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
| 438 |
> |
undergoes two separate reconstructions upon CO adsorption.\cite{Tao:2010} |
| 439 |
> |
The first involves a doubling of the step height and plateau length. |
| 440 |
> |
Similar behavior has been seen on numerous surfaces |
| 441 |
> |
at varying conditions: Ni(977), Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 442 |
> |
Of the two systems we examined, the Pt system showed a greater |
| 443 |
> |
propensity for reconstruction when compared to the Au system |
| 444 |
> |
because of the larger surface mobility and extent of step wandering. |
| 445 |
> |
The amount of reconstruction is strongly correlated to the amount of CO |
| 446 |
> |
adsorbed upon the surface. This appears to be related to the |
| 447 |
> |
effect that adsorbate coverage has on edge breakup and on the |
| 448 |
> |
surface diffusion of metal adatoms. While both systems displayed |
| 449 |
> |
step-edge wandering, only the 50\% Pt surface underwent the |
| 450 |
> |
doubling seen by Tao et al.\cite{Tao:2010} within the time scales studied here. |
| 451 |
> |
Over longer periods, (150~ns) two more double layers formed |
| 452 |
> |
on this interface. Although double layer formation did not occur |
| 453 |
> |
in the other Pt systems, they show more step-wandering and |
| 454 |
> |
general roughening compared to their Au counterparts. The |
| 455 |
> |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 456 |
> |
various times along the simulation showing the evolution of a double layer step-edge. |
| 457 |
|
|
| 458 |
+ |
The second reconstruction on the Pt(557) surface observed by |
| 459 |
+ |
Tao involved the formation of triangular clusters that stretched |
| 460 |
+ |
across the plateau between two step-edges. Neither system, within |
| 461 |
+ |
the 40~ns time scale or the extended simulation time of 150~ns for |
| 462 |
+ |
the 50\% Pt system, experienced this reconstruction. |
| 463 |
|
|
| 464 |
+ |
%Evolution of surface |
| 465 |
+ |
\begin{figure}[H] |
| 466 |
+ |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 467 |
+ |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 468 |
+ |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 469 |
+ |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 470 |
+ |
doubling of the layers appears only after two adjacent step-edges |
| 471 |
+ |
touch. The circled spot in (b) nucleated the growth of the double |
| 472 |
+ |
step observed in the later configurations.} |
| 473 |
+ |
\label{fig:reconstruct} |
| 474 |
+ |
\end{figure} |
| 475 |
|
|
| 476 |
+ |
\subsection{Dynamics} |
| 477 |
+ |
Previous atomistic simulations of stepped surfaces dealt largely |
| 478 |
+ |
with the energetics and structures at different conditions |
| 479 |
+ |
\cite{Williams:1991,Williams:1994}. Consequently, the most common |
| 480 |
+ |
technique utilized to date has been Monte Carlo sampling. Monte Carlo approaches give an efficient |
| 481 |
+ |
sampling of the equilibrium thermodynamic landscape at the expense |
| 482 |
+ |
of ignoring the dynamics of the system. Previous experimental work by Pearl and |
| 483 |
+ |
Sibener\cite{Pearl}, using STM, has been able to capture the coalescing |
| 484 |
+ |
of steps on Ni(977). The time scale of the image acquisition, |
| 485 |
+ |
$\sim$70~s/image provides an upper bound for the time required for |
| 486 |
+ |
the doubling to occur. By utilizing Molecular Dynamics we were able to probe the dynamics of these reconstructions and in this section we give data on dynamic and |
| 487 |
+ |
transport properties, e.g. diffusion, layer formation time, etc. |
| 488 |
+ |
|
| 489 |
+ |
|
| 490 |
+ |
\subsubsection{Transport of surface metal atoms} |
| 491 |
+ |
%forcedSystems/stepSeparation |
| 492 |
+ |
The movement or wandering of a step-edge is a cooperative effect |
| 493 |
+ |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 494 |
+ |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 495 |
+ |
much surface diffusion because of the large energetic barrier that must |
| 496 |
+ |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 497 |
+ |
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 498 |
+ |
Breaking away from the step-edge on a clean surface still imposes an |
| 499 |
+ |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 500 |
+ |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 501 |
+ |
The penalty lowers significantly when CO is present in sufficient quantities |
| 502 |
+ |
on the surface. For certain distributions of CO, see Figures \ref{fig:sketchGraphic} and \ref{fig:sketchEnergies}, the penalty can fall to as low as |
| 503 |
+ |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 504 |
+ |
diffusion is negligible ( \textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 505 |
+ |
able to explore the terrace before rejoining either their original step-edge or |
| 506 |
+ |
becoming a part of a different edge. It is a difficult process for an atom |
| 507 |
+ |
to traverse to a separate terrace although the presence of CO can lower the |
| 508 |
+ |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 509 |
+ |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 510 |
+ |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 511 |
+ |
observation of the mobile metal atoms showed that they were typically in |
| 512 |
+ |
equilibrium with the step-edges, dynamically breaking apart and rejoining the edges. |
| 513 |
+ |
At times, their motion was concerted and two or more adatoms would be |
| 514 |
+ |
observed moving together across the surfaces. |
| 515 |
+ |
|
| 516 |
+ |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 517 |
+ |
between saved configurations of the system (typically 10-100 ps). An atom that was |
| 518 |
+ |
truly mobile would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 519 |
+ |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 520 |
+ |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 521 |
+ |
local structures and in this work, the presence of single and double layer |
| 522 |
+ |
step-edges causes the diffusion parallel to the step-edges to be larger than |
| 523 |
+ |
the diffusion perpendicular to these edges. Parallel and perpendicular |
| 524 |
+ |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 525 |
+ |
|
| 526 |
+ |
%Diffusion graph |
| 527 |
+ |
\begin{figure}[H] |
| 528 |
+ |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
| 529 |
+ |
\caption{Diffusion constants for mobile surface atoms along directions |
| 530 |
+ |
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 531 |
+ |
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 532 |
+ |
surface coverage. Diffusion parallel to the step-edge is higher |
| 533 |
+ |
than that perpendicular to the edge because of the lower energy |
| 534 |
+ |
barrier associated with traversing along the edge as compared to |
| 535 |
+ |
completely breaking away. The two reported diffusion constants for |
| 536 |
+ |
the 50\% Pt system arise from different sample sets. The lower values |
| 537 |
+ |
correspond to the same 40~ns amount that all of the other systems were |
| 538 |
+ |
examined at, while the larger values correspond to a 20~ns period } |
| 539 |
+ |
\label{fig:diff} |
| 540 |
+ |
\end{figure} |
| 541 |
+ |
|
| 542 |
+ |
The lack of a definite trend in the Au diffusion data in Figure \ref{fig:diff} is likely due |
| 543 |
+ |
to the weaker bonding between Au and CO. This leads to a lower observed |
| 544 |
+ |
coverage ({\it x}-axis) when compared to dosage amount, which |
| 545 |
+ |
then further limits the effect the CO can have on surface diffusion. The correlation |
| 546 |
+ |
between coverage and Pt diffusion rates conversely shows a |
| 547 |
+ |
definite trend marred by the highest coverage surface. Two |
| 548 |
+ |
explanations arise for this drop. First, upon a visual inspection of |
| 549 |
+ |
the system, after a double layer has been formed, it maintains its |
| 550 |
+ |
stability strongly and is no longer a good source for adatoms and so |
| 551 |
+ |
atoms that had been tracked for mobility data have now been buried. By |
| 552 |
+ |
performing the same diffusion calculation but on a shorter run time |
| 553 |
+ |
(20~ns), only including data before the formation of the double layer, we obtain |
| 554 |
+ |
the larger values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$ at the 50\% coverage. |
| 555 |
+ |
This places the parallel diffusion constant more closely in line with the |
| 556 |
+ |
expected trend, while the perpendicular diffusion constant does not |
| 557 |
+ |
drop as far. A secondary explanation arising from our analysis of the |
| 558 |
+ |
mechanism of double layer formation focuses on the effect that CO on the |
| 559 |
+ |
surface has with respect to overcoming surface diffusion of Pt. If the |
| 560 |
+ |
coverage is too sparse, the Pt engages in minimal interactions and |
| 561 |
+ |
thus minimal diffusion. As coverage increases, there are more favorable |
| 562 |
+ |
arrangements of CO on the surface allowing the formation of a path, |
| 563 |
+ |
a minimum energy trajectory, for the adatom to explore the surface. |
| 564 |
+ |
As the CO is constantly moving on the surface, this path is constantly |
| 565 |
+ |
changing. If the coverage becomes too great, the paths could |
| 566 |
+ |
potentially be clogged leading to a decrease in diffusion despite |
| 567 |
+ |
their being more adatoms and step-wandering. |
| 568 |
+ |
|
| 569 |
+ |
|
| 570 |
+ |
|
| 571 |
+ |
\subsubsection{Dynamics of double layer formation} |
| 572 |
+ |
The increased diffusion on Pt at the higher |
| 573 |
+ |
CO coverages plays a primary role in double layer formation. However, this is not |
| 574 |
+ |
a complete explanation -- the 33\%~Pt system |
| 575 |
+ |
has higher diffusion constants but did not show |
| 576 |
+ |
any signs of edge doubling in the observed run time. On the |
| 577 |
+ |
50\%~Pt system, one layer formed within the first 40~ns of simulation time, while two more were formed as the system was run for an additional |
| 578 |
+ |
110~ns (150~ns total). Previous experimental |
| 579 |
+ |
work gives insight into the upper bounds of the |
| 580 |
+ |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 581 |
+ |
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 582 |
+ |
appearance of a double layer, appears at 19~ns |
| 583 |
+ |
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 584 |
+ |
formed the double layer and by 86~ns, the complete layer |
| 585 |
+ |
has been flattened out. The double layer could be considered |
| 586 |
+ |
``complete" by 37~ns but remains a bit rough. From the |
| 587 |
+ |
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 588 |
+ |
$\sim$40~ns was necessary for the layer to completely straighten. |
| 589 |
+ |
The other two layers in this simulation formed over periods of |
| 590 |
+ |
22~ns and 42~ns respectively. Comparing this to the upper |
| 591 |
+ |
bounds of the image scan, it is likely that most aspects of this |
| 592 |
+ |
reconstruction occur very rapidly. A possible explanation |
| 593 |
+ |
for this rapid reconstruction is the elevated temperatures |
| 594 |
+ |
under which our systems were simulated. It is probable that the process would |
| 595 |
+ |
take longer at lower temperatures. |
| 596 |
+ |
|
| 597 |
+ |
|
| 598 |
+ |
|
| 599 |
+ |
|
| 600 |
+ |
|
| 601 |
+ |
|
| 602 |
+ |
%Sketch graphic of different configurations |
| 603 |
+ |
\begin{figure}[H] |
| 604 |
+ |
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
| 605 |
+ |
\caption{The dark grey atoms refer to the upper ledge, while the white atoms are |
| 606 |
+ |
the lower terrace. The blue highlighted atoms had a CO in a vertical atop position |
| 607 |
+ |
upon them. These are a sampling of the configurations examined to gain a more |
| 608 |
+ |
complete understanding of the effects CO has on surface diffusion and edge breakup. |
| 609 |
+ |
Energies associated with each configuration are displayed in Figure \ref{fig:SketchEnergies}.} |
| 610 |
+ |
\label{fig:SketchGraphic} |
| 611 |
+ |
\end{figure} |
| 612 |
+ |
|
| 613 |
+ |
%energy graph corresponding to sketch graphic |
| 614 |
+ |
\begin{figure}[H] |
| 615 |
+ |
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf} |
| 616 |
+ |
\caption{The energy curves directly correspond to the labeled model |
| 617 |
+ |
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
| 618 |
+ |
to their initial configuration so the energy of a and h do not have the |
| 619 |
+ |
same zero value. As is seen, certain arrangements of CO can lower |
| 620 |
+ |
the energetic barrier that must be overcome to create an adatom. |
| 621 |
+ |
However, it is the highest coverages where these higher-energy |
| 622 |
+ |
configurations of CO will be more likely. } |
| 623 |
+ |
\label{fig:SketchEnergies} |
| 624 |
+ |
\end{figure} |
| 625 |
+ |
|
| 626 |
|
%Discussion |
| 627 |
|
\section{Discussion} |
| 628 |
< |
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. |
| 628 |
> |
We have shown that the classical potential models are able to model the initial reconstruction of the |
| 629 |
> |
Pt(557) surface upon CO adsorption as shown by Tao et al. \cite{Tao:2010}. More importantly, we |
| 630 |
> |
were able to observe features of the dynamic processes necessary for this reconstruction. |
| 631 |
|
|
| 632 |
|
\subsection{Diffusion} |
| 633 |
< |
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?) |
| 634 |
< |
\\ |
| 635 |
< |
\\ |
| 636 |
< |
%Evolution of surface |
| 633 |
> |
As shown in Figure \ref{fig:diff}, for the Pt systems, there |
| 634 |
> |
is a strong trend toward higher diffusion constants as |
| 635 |
> |
surface coverage of CO increases. The drop for the 50\% |
| 636 |
> |
case being explained as double layer formation already |
| 637 |
> |
beginning to occur in the analyzed 40~ns, which lowered |
| 638 |
> |
the calculated diffusion rates. Between the parallel and |
| 639 |
> |
perpendicular rates, the perpendicular diffusion constant |
| 640 |
> |
appears to be the most important indicator of double layer |
| 641 |
> |
formation. As highlighted in Figure \ref{fig:reconstruct}, the |
| 642 |
> |
formation of the double layer did not begin until a nucleation |
| 643 |
> |
site appeared. And as mentioned by Williams et al.\cite{Williams:1991, Williams:1994}, |
| 644 |
> |
the inability for edges to cross leads to an effective repulsion. |
| 645 |
> |
This repulsion must be overcome to allow step coalescence. |
| 646 |
> |
A greater $\textbf{D}_\perp$ implies more step-wandering |
| 647 |
> |
and a larger chance for the stochastic meeting of two edges |
| 648 |
> |
to form the nucleation point. Upon that appearance, parallel |
| 649 |
> |
diffusion along the step-edge can help ``zipper'' up the double |
| 650 |
> |
layer. This helps explain why the time scale for formation after |
| 651 |
> |
the appearance of a nucleation site was rapid, while the initial |
| 652 |
> |
appearance of said site was unpredictable. |
| 653 |
> |
|
| 654 |
> |
\subsection{Mechanism for restructuring} |
| 655 |
> |
Since the Au surface showed no large scale restructuring throughout |
| 656 |
> |
our simulation time our discussion will focus on the 50\% Pt-CO system |
| 657 |
> |
which did undergo the doubling featured in Figure \ref{fig:reconstruct}. |
| 658 |
> |
Similarities of our results to those reported previously by Tao et al.\cite{Tao:2010} |
| 659 |
> |
are quite strong. The simulated Pt system exposed to a large dosage |
| 660 |
> |
of CO readily restructures by doubling the terrace widths and step heights. |
| 661 |
> |
The restructuring occurs in a piecemeal fashion, one to two Pt atoms at a |
| 662 |
> |
time, but is rapid on experimental timescales. The adatoms either break |
| 663 |
> |
away from the step-edge and stay on the lower terrace or they lift up onto |
| 664 |
> |
a higher terrace. Once ``free'', they diffuse on the terrace until reaching |
| 665 |
> |
another step-edge or rejoining their original edge. This combination of |
| 666 |
> |
growth and decay of the step-edges is in a state of dynamic equilibrium. |
| 667 |
> |
However, once two previously separated edges meet as shown in Figure 1.B, |
| 668 |
> |
this nucleates the rest of the edge to meet up, forming a double layer. |
| 669 |
> |
From simulations which exhibit a double layer, the time delay from the |
| 670 |
> |
initial appearance of a nucleation point to a fully formed double layer is $\sim$35~ns. |
| 671 |
> |
|
| 672 |
> |
A number of possible mechanisms exist to explain the role of adsorbed |
| 673 |
> |
CO in restructuring the Pt surface. Quadrupolar repulsion between adjacent |
| 674 |
> |
CO molecules adsorbed on the surface is one possibility. However, |
| 675 |
> |
the quadrupole-quadrupole interaction is short-ranged and is attractive for |
| 676 |
> |
some orientations. If the CO molecules are ``locked'' in a specific orientation |
| 677 |
> |
relative to each other, through atop adsorption for example, this explanation |
| 678 |
> |
gains some credence. The energetic repulsion between two CO located a |
| 679 |
> |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both in |
| 680 |
> |
a vertical orientation, is 8.62 kcal/mol. Moving the CO apart to the second |
| 681 |
> |
nearest-neighbor distance of 4.8~\AA~or 5.54~\AA~drops the repulsion to |
| 682 |
> |
nearly 0 kcal/mol. Allowing the CO to rotate away from a purely vertical orientation |
| 683 |
> |
also lowers the repulsion. A minimum of 6.2 kcal/mol is reached at when the |
| 684 |
> |
angle between the 2 CO is $\sim$24\textsuperscript{o}, when the carbons are |
| 685 |
> |
locked at a distance of 2.77 \AA apart. As mentioned above, the energy barrier |
| 686 |
> |
for surface diffusion of a Pt adatom is only 4 kcal/mol. So this repulsion between |
| 687 |
> |
neighboring CO molecules can increase the surface diffusion. However, the |
| 688 |
> |
residence time of CO on Pt was examined and while the majority of the CO is |
| 689 |
> |
on or near the surface throughout the run, the molecules are extremely mobile, |
| 690 |
> |
with diffusion constants 40 to 2500 times larger, depending on coverage. This |
| 691 |
> |
mobility suggests that the CO are more likely to shift their positions without |
| 692 |
> |
necessarily the Pt along with them. |
| 693 |
> |
|
| 694 |
> |
Another possible and more likely mechanism for the restructuring is in the |
| 695 |
> |
destabilization of strong Pt-Pt interactions by CO adsorbed on surface |
| 696 |
> |
Pt atoms. To test this hypothesis, numerous configurations of |
| 697 |
> |
CO in varying quantities were arranged on the higher and lower plateaus |
| 698 |
> |
around a step on a otherwise clean Pt(557) surface. A few sample |
| 699 |
> |
configurations are displayed in Figure \ref{fig:lambdaTable}, with |
| 700 |
> |
energies at various positions along the path displayed in Table |
| 701 |
> |
\ref{tab:rxcoord}. Certain configurations of CO, cases B and D for |
| 702 |
> |
example, can have quite strong energetic reasons for breaking |
| 703 |
> |
away from the step-edge. Although the packing of these configurations |
| 704 |
> |
is unlikely until CO coverage has reached a high enough value. |
| 705 |
> |
These examples are showing the most difficult cases, immediate |
| 706 |
> |
adatom formation through breakage away from the step-edge, which |
| 707 |
> |
is why their energies at large distances are relatively high. There are |
| 708 |
> |
mechanistic paths where an edge atom could get shifted to onto the |
| 709 |
> |
step-edge to form a small peak before fully breaking away. And again, |
| 710 |
> |
once the adatom is formed, the barrier for diffusion on the surface is |
| 711 |
> |
negligible. These sample configurations help explain CO's effect on |
| 712 |
> |
general surface mobility and step wandering, but they are lacking in |
| 713 |
> |
providing a mechanism for the formation of double layers. One possible |
| 714 |
> |
mechanism is elucidated in Figure \ref{fig:lambda}, where a burrowing |
| 715 |
> |
and lifting process of an adatom and step-edge atom respectively is |
| 716 |
> |
examined. The system, without CO present, is nearly energetically |
| 717 |
> |
neutral, whereas with CO present there is a $\sim$ 15 kcal/mol drop |
| 718 |
> |
in the energy of the system. |
| 719 |
> |
|
| 720 |
> |
%lambda progression of Pt -> shoving its way into the step |
| 721 |
|
\begin{figure}[H] |
| 722 |
< |
\includegraphics[scale=0.5]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 723 |
< |
\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.} |
| 722 |
> |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 723 |
> |
\caption{A model system of the Pt(557) surface was used as the framework |
| 724 |
> |
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 725 |
> |
placements, and rotations of CO were examined as they affect Pt movement. |
| 726 |
> |
The coordinate displayed in this Figure was a representative run. relative to the energy of the system at 0\%, there |
| 727 |
> |
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 728 |
> |
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 729 |
> |
\label{fig:lambda} |
| 730 |
|
\end{figure} |
| 731 |
|
|
| 732 |
|
|
| 733 |
|
|
| 734 |
|
|
| 191 |
– |
%Peaks! |
| 192 |
– |
\includegraphics[scale=0.25]{doublePeaks_noCO.png} |
| 193 |
– |
\section{Conclusion} |
| 735 |
|
|
| 736 |
+ |
%breaking of the double layer upon removal of CO |
| 737 |
+ |
\begin{figure}[H] |
| 738 |
+ |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 739 |
+ |
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 740 |
+ |
helped maintain the stability of the double layer and upon removal the two layers break |
| 741 |
+ |
and begin separating. The separation is not a simple pulling apart however, rather |
| 742 |
+ |
there is a mixing of the lower and upper atoms at the edge.} |
| 743 |
+ |
\label{fig:breaking} |
| 744 |
+ |
\end{figure} |
| 745 |
|
|
| 746 |
|
|
| 747 |
|
|
| 748 |
|
|
| 749 |
+ |
%Peaks! |
| 750 |
+ |
%\begin{figure}[H] |
| 751 |
+ |
%\includegraphics[width=\linewidth]{doublePeaks_noCO.png} |
| 752 |
+ |
%\caption{At the initial formation of this double layer ( $\sim$ 37 ns) there is a degree |
| 753 |
+ |
%of roughness inherent to the edge. The next $\sim$ 40 ns show the edge with |
| 754 |
+ |
%aspects of waviness and by 80 ns the double layer is completely formed and smooth. } |
| 755 |
+ |
%\label{fig:peaks} |
| 756 |
+ |
%\end{figure} |
| 757 |
|
|
| 758 |
|
|
| 759 |
+ |
%Don't think I need this |
| 760 |
+ |
%clean surface... |
| 761 |
+ |
%\begin{figure}[H] |
| 762 |
+ |
%\includegraphics[width=\linewidth]{557_300K_cleanPDF.pdf} |
| 763 |
+ |
%\caption{} |
| 764 |
|
|
| 765 |
+ |
%\end{figure} |
| 766 |
+ |
%\label{fig:clean} |
| 767 |
|
|
| 768 |
|
|
| 769 |
+ |
\section{Conclusion} |
| 770 |
+ |
In this work we have shown the reconstruction of the Pt(557) crystalline surface upon adsorption of CO in less than a $\mu s$. Only the highest coverage Pt system showed this initial reconstruction similar to that seen previously. The strong interaction between Pt and CO and the limited interaction between Au and CO helps explain the differences between the two systems. |
| 771 |
|
|
| 772 |
< |
\end{document} |
| 772 |
> |
%Things I am not ready to remove yet |
| 773 |
> |
|
| 774 |
> |
%Table of Diffusion Constants |
| 775 |
> |
%Add gold?M |
| 776 |
> |
% \begin{table}[H] |
| 777 |
> |
% \caption{} |
| 778 |
> |
% \centering |
| 779 |
> |
% \begin{tabular}{| c | cc | cc | } |
| 780 |
> |
% \hline |
| 781 |
> |
% &\multicolumn{2}{c|}{\textbf{Platinum}}&\multicolumn{2}{c|}{\textbf{Gold}} \\ |
| 782 |
> |
% \hline |
| 783 |
> |
% \textbf{Surface Coverage} & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ & $\mathbf{D}_{\parallel}$ & $\mathbf{D}_{\perp}$ \\ |
| 784 |
> |
% \hline |
| 785 |
> |
% 50\% & 4.32(2) & 1.185(8) & 1.72(2) & 0.455(6) \\ |
| 786 |
> |
% 33\% & 5.18(3) & 1.999(5) & 1.95(2) & 0.337(4) \\ |
| 787 |
> |
% 25\% & 5.01(2) & 1.574(4) & 1.26(3) & 0.377(6) \\ |
| 788 |
> |
% 5\% & 3.61(2) & 0.355(2) & 1.84(3) & 0.169(4) \\ |
| 789 |
> |
% 0\% & 3.27(2) & 0.147(4) & 1.50(2) & 0.194(2) \\ |
| 790 |
> |
% \hline |
| 791 |
> |
% \end{tabular} |
| 792 |
> |
% \end{table} |
| 793 |
> |
|
| 794 |
> |
\begin{acknowledgement} |
| 795 |
> |
Support for this project was provided by the National Science |
| 796 |
> |
Foundation under grant CHE-0848243 and by the Center for Sustainable |
| 797 |
> |
Energy at Notre Dame (cSEND). Computational time was provided by the |
| 798 |
> |
Center for Research Computing (CRC) at the University of Notre Dame. |
| 799 |
> |
\end{acknowledgement} |
| 800 |
> |
\newpage |
| 801 |
> |
\bibliography{firstTryBibliography} |
| 802 |
> |
%\end{doublespace} |
| 803 |
> |
|
| 804 |
> |
\begin{tocentry} |
| 805 |
> |
%\includegraphics[height=3.5cm]{timelapse} |
| 806 |
> |
\end{tocentry} |
| 807 |
> |
|
| 808 |
> |
\end{document} |
