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\usepackage{graphicx} |
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\usepackage{multirow} |
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\usepackage{multicol} |
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\usepackage{epstopdf} |
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|
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\usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions |
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% \usepackage[square, comma, sort&compress]{natbib} |
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\usepackage{url} |
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\pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm |
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\evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight |
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9.0in \textwidth 6.5in \brokenpenalty=10000 |
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9.0in \textwidth 6.5in \brokenpenalty=1110000 |
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|
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% double space list of tables and figures |
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%\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}} |
| 87 |
|
is sufficient to explain the reconstructions observed on the Pt |
| 88 |
|
systems and the lack of reconstruction of the Au systems. |
| 89 |
|
|
| 90 |
+ |
|
| 91 |
+ |
The mechanism and dynamics of surface reconstructions of Pt(557) |
| 92 |
+ |
and Au(557) exposed to various coverages of carbon monoxide (CO) |
| 93 |
+ |
were investigated using molecular dynamics simulations. Metal-CO |
| 94 |
+ |
interactions were parameterized from experimental data and plane-wave |
| 95 |
+ |
Density Functional Theory (DFT) calculations. The large difference in |
| 96 |
+ |
binding strengths of the Pt-CO and Au-CO interactions was found to play |
| 97 |
+ |
a significant role in step-edge stability and adatom diffusion constants. |
| 98 |
+ |
The energetics of CO adsorbed to the surface is sufficient to explain the |
| 99 |
+ |
step-doubling reconstruction observed on Pt(557) and the lack of such |
| 100 |
+ |
a reconstruction on the Au(557) surface. |
| 101 |
|
\end{abstract} |
| 102 |
|
|
| 103 |
|
\newpage |
| 173 |
|
Coulomb potential. For this work, we have used classical molecular |
| 174 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 175 |
|
for transition metals. In particular, we used the EAM potential for |
| 176 |
< |
Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid |
| 176 |
> |
Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid |
| 177 |
|
three-site model developed by Straub and Karplus for studying |
| 178 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 179 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 186 |
|
methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
| 187 |
|
but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
| 188 |
|
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
| 189 |
< |
parameter sets. The glue model of Ercolessi {\it et al}. is among the |
| 190 |
< |
fastest of these density functional approaches.\cite{Ercolessi88} In |
| 189 |
> |
parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the |
| 190 |
> |
fastest of these density functional approaches. In |
| 191 |
|
all of these models, atoms are treated as a positively charged |
| 192 |
|
core with a radially-decaying valence electron distribution. To |
| 193 |
|
calculate the energy for embedding the core at a particular location, |
| 472 |
|
|
| 473 |
|
%Evolution of surface |
| 474 |
|
\begin{figure}[H] |
| 475 |
< |
\includegraphics[width=\linewidth]{ProgressionOfDoubleLayerFormation_yellowCircle.png} |
| 475 |
> |
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation.pdf} |
| 476 |
|
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 477 |
|
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 478 |
|
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 531 |
|
|
| 532 |
|
%Diffusion graph |
| 533 |
|
\begin{figure}[H] |
| 534 |
< |
\includegraphics[width=\linewidth]{DiffusionComparison_errorXY_remade_20ns.pdf} |
| 534 |
> |
\includegraphics[width=\linewidth]{Portrait_DiffusionComparison_1.pdf} |
| 535 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 536 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 537 |
|
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 612 |
|
\subsection{Mechanism for restructuring} |
| 613 |
|
Since the Au surface showed no large scale restructuring in any of |
| 614 |
|
our simulations, our discussion will focus on the 50\% Pt-CO system |
| 615 |
< |
which did exhibit doubling featured in Figure \ref{fig:reconstruct}. A |
| 615 |
> |
which did exhibit doubling. A |
| 616 |
|
number of possible mechanisms exist to explain the role of adsorbed |
| 617 |
|
CO in restructuring the Pt surface. Quadrupolar repulsion between |
| 618 |
|
adjacent CO molecules adsorbed on the surface is one possibility. |
| 619 |
|
However, the quadrupole-quadrupole interaction is short-ranged and |
| 620 |
|
is attractive for some orientations. If the CO molecules are ``locked'' in |
| 621 |
|
a specific orientation relative to each other, through atop adsorption for |
| 622 |
< |
example, this explanation would gain credence. The energetic repulsion |
| 622 |
> |
example, this explanation would gain credence. The calculated energetic repulsion |
| 623 |
|
between two CO molecules located a distance of 2.77~\AA~apart |
| 624 |
|
(nearest-neighbor distance of Pt) and both in a vertical orientation, |
| 625 |
|
is 8.62 kcal/mol. Moving the CO to the second nearest-neighbor distance |
| 627 |
|
from a purely vertical orientation also lowers the repulsion. When the |
| 628 |
|
carbons are locked at a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is |
| 629 |
|
reached when the angle between the 2 CO is $\sim$24\textsuperscript{o}. |
| 630 |
< |
The barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 631 |
< |
repulsion between adjacent CO molecules could increase the surface |
| 630 |
> |
The calculated barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 631 |
> |
repulsion between adjacent CO molecules bound to Pt could increase the surface |
| 632 |
|
diffusion. However, the residence time of CO on Pt suggests that these |
| 633 |
|
molecules are extremely mobile, with diffusion constants 40 to 2500 times |
| 634 |
< |
larger than surface Pt atoms. This mobility suggests that the CO are more |
| 635 |
< |
likely to shift their positions without dragging the Pt along with them. |
| 634 |
> |
larger than surface Pt atoms. This mobility suggests that the CO molecules jump |
| 635 |
> |
between different Pt atoms throughout the simulation, but will stay bound for |
| 636 |
> |
significant periods of time. |
| 637 |
|
|
| 638 |
< |
Another possible mechanism for the restructuring is in the destabilization of strong Pt-Pt interactions by CO adsorbed on surface Pt atoms. To test this hypothesis, a number of configurations of CO in varying quantities were arranged on the upper plateaus around a step on an otherwise clean Pt(557) surface. A few sample configurations are displayed in Figure \ref{fig:SketchGraphic}, with energy curves corresponding to each configuration in Figure \ref{fig:SketchEnergies}. Certain configurations of CO, cases (e), (g) and (h) for example, can provide significant energetic pushes for Pt atoms to break away from the step-edge. |
| 638 |
> |
A different interpretation of the above mechanism, taking into account the large |
| 639 |
> |
mobility of the CO, looks at how instantaneous and short-lived configurations of |
| 640 |
> |
CO on the surface can destabilize Pt-Pt interactions leading to increased step-edge |
| 641 |
> |
breakup and diffusion. On the bare Pt(557) surface the barrier to completely detach |
| 642 |
> |
an edge atom is $\sim$43~kcal/mol, as is shown in configuration (a) in Figures |
| 643 |
> |
\ref{fig:SketchGraphic} \& \ref{fig:SketchEnergies}. For certain configurations, cases |
| 644 |
> |
(e), (g), and (h), the barrier can be lowered to $\sim$23~kcal/mole. In these instances, |
| 645 |
> |
it becomes quite energetically favorable to roughen the edge by introducing a small |
| 646 |
> |
separation of 0.5 to 1.0~\AA. This roughening becomes immediately obvious in |
| 647 |
> |
simulations with significant CO populations. The roughening is present to a lesser extent |
| 648 |
> |
on lower coverage surfaces and even on the bare surfaces, although in these cases it is likely |
| 649 |
> |
due to stochastic vibrational processes that squeeze out step-edge atoms. The mechanism |
| 650 |
> |
of step-edge breakup suggested by these energy curves is one of the most difficult |
| 651 |
> |
processes, a complete break-away from the step-edge in one unbroken movement. |
| 652 |
> |
Easier multistep mechanisms likely exist where an adatom moves laterally on the surface |
| 653 |
> |
after being ejected so it ends up alongside the ledge. This provides the atom with 5 nearest |
| 654 |
> |
neighbors, which while lower than the 7 if it had stayed a part of the step-edge, is higher |
| 655 |
> |
than the 3 it could maintain located on the terrace. In this proposed mechanism, the CO |
| 656 |
> |
quadrupolar repulsion is still playing a primary role, but for its importance in roughening |
| 657 |
> |
the step-edge, rather than maintaining long-term bonds with a single Pt atom which is not |
| 658 |
> |
born out by their mobility data. The requirement for a large density of CO on the surface |
| 659 |
> |
for some of the more favorable suggested configurations in Figure \ref{fig:SketchGraphic} |
| 660 |
> |
correspond well with the increased mobility seen on higher coverage surfaces. |
| 661 |
|
|
| 627 |
– |
|
| 662 |
|
%Sketch graphic of different configurations |
| 663 |
|
\begin{figure}[H] |
| 664 |
|
\includegraphics[width=0.8\linewidth, height=0.8\textheight]{COpathsSketch.pdf} |
| 672 |
|
|
| 673 |
|
%energy graph corresponding to sketch graphic |
| 674 |
|
\begin{figure}[H] |
| 675 |
< |
\includegraphics[width=\linewidth]{stepSeparationComparison.pdf} |
| 675 |
> |
\includegraphics[width=\linewidth]{Portrait_SeparationComparison.pdf} |
| 676 |
|
\caption{The energy curves directly correspond to the labeled model |
| 677 |
|
surface in Figure \ref{fig:SketchGraphic}. All energy curves are relative |
| 678 |
|
to their initial configuration so the energy of a and h do not have the |
| 683 |
|
\label{fig:SketchEnergies} |
| 684 |
|
\end{figure} |
| 685 |
|
|
| 686 |
< |
|
| 686 |
> |
While configurations of CO on the surface are able to increase diffusion, |
| 687 |
> |
this does not immediately provide an explanation for the formation of double |
| 688 |
> |
layers. If adatoms were constrained to their terrace then doubling would be |
| 689 |
> |
much less likely to occur. Nucleation sites could still potentially form, but there |
| 690 |
> |
would not be enough atoms to finish the doubling. For a non-simulated metal surface, where the |
| 691 |
> |
step lengths can be assumed to be infinite relative to atomic sizes, local doubling would be possible, but in |
| 692 |
> |
our simulations with our periodic treatment of the system, the system is not large enough to experience this effect. |
| 693 |
> |
Thus, there must be a mechanism that explains how adatoms are able to move |
| 694 |
> |
amongst terraces. Figure \ref{fig:lambda} shows points along a reaction coordinate |
| 695 |
> |
where an adatom along the step-edge with an adsorbed CO ``burrows'' into the |
| 696 |
> |
edge displacing an atom onto the higher terrace. This mechanism was chosen |
| 697 |
> |
because of similar events that were observed during the simulations. The barrier |
| 698 |
> |
heights we obtained are only approximations because we constrained the movement |
| 699 |
> |
of the highlighted atoms along a specific concerted path. The calculated $\Delta E$'s |
| 700 |
> |
are provide a strong energetic support for this modeled lifting mechanism. When CO is not present and |
| 701 |
> |
this reaction coordinate is followed, the $\Delta E > 3$~kcal/mol. The example shown |
| 702 |
> |
in the figure, where CO is present in the atop position, has a $\Delta E < -15$~kcal/mol. |
| 703 |
> |
While the barrier height is comparable for both cases, there is nearly a 20~kcal/mol |
| 704 |
> |
difference in energies and makes the process energetically favorable. |
| 705 |
|
|
| 706 |
|
%lambda progression of Pt -> shoving its way into the step |
| 707 |
|
\begin{figure}[H] |
| 708 |
< |
\includegraphics[width=\linewidth]{lambdaProgression_atopCO_withLambda.png} |
| 709 |
< |
\caption{A model system of the Pt(557) surface was used as the framework |
| 710 |
< |
for exploring energy barriers along a reaction coordinate. Various numbers, |
| 711 |
< |
placements, and rotations of CO were examined as they affect Pt movement. |
| 712 |
< |
The coordinate displayed in this Figure was a representative run. relative to the energy of the system at 0\%, there |
| 661 |
< |
is a slight decrease upon insertion of the Pt atom into the step-edge along |
| 662 |
< |
with the resultant lifting of the other Pt atom when CO is present at certain positions.} |
| 708 |
> |
\includegraphics[width=\linewidth]{EPS_rxnCoord.pdf} |
| 709 |
> |
\caption{ Various points along a reaction coordinate are displayed in the figure. |
| 710 |
> |
The mechanism of edge traversal is examined in the presence of CO. The approximate |
| 711 |
> |
barrier for the displayed process is 20~kcal/mol. However, the $\Delta E$ of this process |
| 712 |
> |
is -15~kcal/mol making it an energetically favorable process.} |
| 713 |
|
\label{fig:lambda} |
| 714 |
|
\end{figure} |
| 715 |
|
|
| 716 |
+ |
The mechanism for doubling on this surface appears to require the cooperation of at least |
| 717 |
+ |
these two described processes. For complete doubling of a layer to occur there must |
| 718 |
+ |
be the equivalent removal of a separate terrace. For those atoms to ``disappear'' from |
| 719 |
+ |
that terrace they must either rise up on the ledge above them or drop to the ledge below |
| 720 |
+ |
them. The presence of CO helps with the energetics of both of these situations. There must be sufficient |
| 721 |
+ |
breakage of the step-edge to increase the concentration of adatoms on the surface and |
| 722 |
+ |
these adatoms must then undergo the burrowing highlighted above or some comparable |
| 723 |
+ |
mechanism to traverse the step-edge. Over time, these mechanisms working in concert |
| 724 |
+ |
lead to the formation of a double layer. |
| 725 |
+ |
|
| 726 |
|
\subsection{CO Removal and double layer stability} |
| 727 |
|
Once a double layer had formed on the 50\%~Pt system it |
| 728 |
|
remained for the rest of the simulation time with minimal |
| 747 |
|
|
| 748 |
|
|
| 749 |
|
|
| 690 |
– |
|
| 691 |
– |
|
| 692 |
– |
|
| 750 |
|
%breaking of the double layer upon removal of CO |
| 751 |
|
\begin{figure}[H] |
| 752 |
< |
\includegraphics[width=\linewidth]{doubleLayerBreaking_greenBlue_whiteLetters.png} |
| 752 |
> |
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking.pdf} |
| 753 |
|
\caption{(A) 0~ps, (B) 100~ps, (C) 1~ns, after the removal of CO. The presence of the CO |
| 754 |
< |
helped maintain the stability of the double layer and upon removal the two layers break |
| 755 |
< |
and begin separating. The separation is not a simple pulling apart however, rather |
| 756 |
< |
there is a mixing of the lower and upper atoms at the edge.} |
| 754 |
> |
helped maintain the stability of the double layer and its microfaceting of the double layer |
| 755 |
> |
into a (111) configuration. This microfacet immediately reverts to the original (100) step |
| 756 |
> |
edge which is a hallmark of the (557) surface. The separation is not a simple sliding apart, rather |
| 757 |
> |
there is a mixing of the lower and upper atoms at the edge.} |
| 758 |
|
\label{fig:breaking} |
| 759 |
|
\end{figure} |
| 760 |
|
|
| 782 |
|
|
| 783 |
|
|
| 784 |
|
\section{Conclusion} |
| 785 |
< |
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. |
| 785 |
> |
The strength of the Pt-CO binding interaction as well as the large |
| 786 |
> |
quadrupolar repulsion between CO molecules are sufficient to |
| 787 |
> |
explain the observed increase in surface mobility and the resultant |
| 788 |
> |
reconstructions at the highest simulated coverage. The weaker |
| 789 |
> |
Au-CO interaction results in lower diffusion constants, less step-wandering, |
| 790 |
> |
and a lack of the double layer reconstruction. An in-depth examination |
| 791 |
> |
of the energetics shows the important role CO plays in increasing |
| 792 |
> |
step-breakup and in facilitating edge traversal which are both |
| 793 |
> |
necessary for double layer formation. |
| 794 |
|
|
| 795 |
+ |
|
| 796 |
+ |
|
| 797 |
|
%Things I am not ready to remove yet |
| 798 |
|
|
| 799 |
|
%Table of Diffusion Constants |
