| 1 |
|
\documentclass[journal = jpccck, manuscript = article]{achemso} |
| 2 |
|
\setkeys{acs}{usetitle = true} |
| 3 |
|
\usepackage{achemso} |
| 4 |
– |
\usepackage{caption} |
| 5 |
– |
\usepackage{float} |
| 6 |
– |
\usepackage{geometry} |
| 4 |
|
\usepackage{natbib} |
| 8 |
– |
\usepackage{setspace} |
| 9 |
– |
\usepackage{xkeyval} |
| 10 |
– |
%%%%%%%%%%%%%%%%%%%%%%% |
| 11 |
– |
\usepackage{amsmath} |
| 12 |
– |
\usepackage{amssymb} |
| 13 |
– |
\usepackage{times} |
| 14 |
– |
\usepackage{mathptm} |
| 15 |
– |
\usepackage{setspace} |
| 16 |
– |
\usepackage{endfloat} |
| 17 |
– |
\usepackage{caption} |
| 18 |
– |
\usepackage{tabularx} |
| 19 |
– |
\usepackage{longtable} |
| 20 |
– |
\usepackage{graphicx} |
| 5 |
|
\usepackage{multirow} |
| 22 |
– |
\usepackage{multicol} |
| 6 |
|
\usepackage{wrapfig} |
| 7 |
< |
\mciteErrorOnUnknownfalse |
| 8 |
< |
%\usepackage{epstopdf} |
| 7 |
> |
\usepackage{fixltx2e} |
| 8 |
> |
%\mciteErrorOnUnknownfalse |
| 9 |
|
|
| 10 |
|
\usepackage[version=3]{mhchem} % this is a great package for formatting chemical reactions |
| 28 |
– |
% \usepackage[square, comma, sort&compress]{natbib} |
| 11 |
|
\usepackage{url} |
| 30 |
– |
\pagestyle{plain} \pagenumbering{arabic} \oddsidemargin 0.0cm |
| 31 |
– |
\evensidemargin 0.0cm \topmargin -21pt \headsep 10pt \textheight |
| 32 |
– |
9.0in \textwidth 6.5in \brokenpenalty=1110000 |
| 12 |
|
|
| 34 |
– |
% double space list of tables and figures |
| 35 |
– |
%\AtBeginDelayedFloats{\renewcomand{\baselinestretch}{1.66}} |
| 36 |
– |
\setlength{\abovecaptionskip}{20 pt} |
| 37 |
– |
\setlength{\belowcaptionskip}{30 pt} |
| 38 |
– |
% \bibpunct{}{}{,}{s}{}{;} |
| 39 |
– |
|
| 40 |
– |
%\citestyle{nature} |
| 41 |
– |
% \bibliographystyle{achemso} |
| 42 |
– |
|
| 13 |
|
\title{Molecular Dynamics simulations of the surface reconstructions |
| 14 |
|
of Pt(557) and Au(557) under exposure to CO} |
| 15 |
|
|
| 48 |
|
\begin{abstract} |
| 49 |
|
The mechanism and dynamics of surface reconstructions of Pt(557) and |
| 50 |
|
Au(557) exposed to various coverages of carbon monoxide (CO) were |
| 51 |
< |
investigated using molecular dynamics simulations. Metal-CO |
| 51 |
> |
investigated using molecular dynamics simulations. Metal-CO |
| 52 |
|
interactions were parameterized from experimental data and |
| 53 |
|
plane-wave Density Functional Theory (DFT) calculations. The large |
| 54 |
|
difference in binding strengths of the Pt-CO and Au-CO interactions |
| 57 |
|
wandering and step doubling were investigated on the Pt(557) |
| 58 |
|
surface. We find that the energetics of CO adsorbed to the surface |
| 59 |
|
can explain the step-doubling reconstruction observed on Pt(557) and |
| 60 |
< |
the lack of such a reconstruction on the Au(557) surface. |
| 60 |
> |
the lack of such a reconstruction on the Au(557) surface. However, |
| 61 |
> |
more complicated reconstructions into triangular clusters that have |
| 62 |
> |
been seen in recent experiments were not observed in these |
| 63 |
> |
simulations. |
| 64 |
|
\end{abstract} |
| 65 |
|
|
| 66 |
|
\newpage |
| 92 |
|
reversible restructuring under exposure to moderate pressures of |
| 93 |
|
carbon monoxide.\cite{Tao:2010} |
| 94 |
|
|
| 95 |
< |
This work is an investigation into the mechanism and timescale for the Pt(557) \& Au(557) |
| 96 |
< |
surface restructuring using molecular simulations. Since the dynamics |
| 97 |
< |
of the process are of particular interest, we employ classical force |
| 98 |
< |
fields that represent a compromise between chemical accuracy and the |
| 99 |
< |
computational efficiency necessary to simulate the process of interest. |
| 100 |
< |
Since restructuring typically occurs as a result of specific interactions of the |
| 101 |
< |
catalyst with adsorbates, in this work, two metal systems exposed |
| 102 |
< |
to carbon monoxide were examined. The Pt(557) surface has already been shown |
| 103 |
< |
to undergo a large scale reconstruction under certain conditions.\cite{Tao:2010} |
| 104 |
< |
The Au(557) surface, because of a weaker interaction with CO, is less |
| 105 |
< |
likely to undergo this kind of reconstruction. However, Peters {\it et al}.\cite{Peters:2000} |
| 106 |
< |
and Piccolo {\it et al}.\cite{Piccolo:2004} have both observed CO-induced |
| 107 |
< |
reconstruction of a Au(111) surface. Peters {\it et al}. saw a relaxation to the |
| 108 |
< |
22 x $\sqrt{3}$ cell. They argued that only a few Au atoms |
| 109 |
< |
become adatoms, limiting the stress of this reconstruction, while |
| 110 |
< |
allowing the rest to relax and approach the ideal (111) |
| 111 |
< |
configuration. They did not see the usual herringbone pattern on Au(111) being greatly |
| 112 |
< |
affected by this relaxation. Piccolo {\it et al}. on the other hand, did see a |
| 113 |
< |
disruption of the herringbone pattern as CO was adsorbed to the |
| 114 |
< |
surface. Both groups suggested that the preference CO shows for |
| 115 |
< |
low-coordinated Au atoms was the primary driving force for the reconstruction. |
| 95 |
> |
This work is an investigation into the mechanism and timescale for the |
| 96 |
> |
Pt(557) \& Au(557) surface restructuring using molecular simulation. |
| 97 |
> |
Since the dynamics of the process are of particular interest, we |
| 98 |
> |
employ classical force fields that represent a compromise between |
| 99 |
> |
chemical accuracy and the computational efficiency necessary to |
| 100 |
> |
simulate the process of interest. Since restructuring typically |
| 101 |
> |
occurs as a result of specific interactions of the catalyst with |
| 102 |
> |
adsorbates, in this work, two metal systems exposed to carbon monoxide |
| 103 |
> |
were examined. The Pt(557) surface has already been shown to undergo a |
| 104 |
> |
large scale reconstruction under certain conditions.\cite{Tao:2010} |
| 105 |
> |
The Au(557) surface, because of weaker interactions with CO, is less |
| 106 |
> |
likely to undergo this kind of reconstruction. However, Peters {\it et |
| 107 |
> |
al}.\cite{Peters:2000} and Piccolo {\it et al}.\cite{Piccolo:2004} |
| 108 |
> |
have both observed CO-induced modification of reconstructions to the |
| 109 |
> |
Au(111) surface. Peters {\it et al}. observed the Au(111)-($22 \times |
| 110 |
> |
\sqrt{3}$) ``herringbone'' reconstruction relaxing slightly under CO |
| 111 |
> |
adsorption. They argued that only a few Au atoms become adatoms, |
| 112 |
> |
limiting the stress of this reconstruction, while allowing the rest to |
| 113 |
> |
relax and approach the ideal (111) configuration. Piccolo {\it et |
| 114 |
> |
al}. on the other hand, saw a more significant disruption of the |
| 115 |
> |
Au(111)-($22 \times \sqrt{3}$) herringbone pattern as CO adsorbed on |
| 116 |
> |
the surface. Both groups suggested that the preference CO shows for |
| 117 |
> |
low-coordinated Au atoms was the primary driving force for the |
| 118 |
> |
relaxation. Although the Au(111) reconstruction was not the primary |
| 119 |
> |
goal of our work, the classical models we have fit may be of future |
| 120 |
> |
use in simulating this reconstruction. |
| 121 |
|
|
| 144 |
– |
|
| 145 |
– |
|
| 122 |
|
%Platinum molecular dynamics |
| 123 |
|
%gold molecular dynamics |
| 124 |
|
|
| 125 |
|
\section{Simulation Methods} |
| 126 |
< |
The challenge in modeling any solid/gas interface is the |
| 127 |
< |
development of a sufficiently general yet computationally tractable |
| 128 |
< |
model of the chemical interactions between the surface atoms and |
| 129 |
< |
adsorbates. Since the interfaces involved are quite large (10$^3$ - |
| 130 |
< |
10$^4$ atoms) and respond slowly to perturbations, {\it ab initio} |
| 126 |
> |
The challenge in modeling any solid/gas interface is the development |
| 127 |
> |
of a sufficiently general yet computationally tractable model of the |
| 128 |
> |
chemical interactions between the surface atoms and adsorbates. Since |
| 129 |
> |
the interfaces involved are quite large (10$^3$ - 10$^4$ atoms), have |
| 130 |
> |
many electrons, and respond slowly to perturbations, {\it ab initio} |
| 131 |
|
molecular dynamics |
| 132 |
|
(AIMD),\cite{KRESSE:1993ve,KRESSE:1993qf,KRESSE:1994ul} Car-Parrinello |
| 133 |
|
methods,\cite{CAR:1985bh,Izvekov:2000fv,Guidelli:2000fy} and quantum |
| 139 |
|
Coulomb potential. For this work, we have used classical molecular |
| 140 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 141 |
|
for transition metals. In particular, we used the EAM potential for |
| 142 |
< |
Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using a rigid |
| 143 |
< |
three-site model developed by Straub and Karplus for studying |
| 142 |
> |
Au-Au and Pt-Pt interactions.\cite{Foiles86} The CO was modeled using |
| 143 |
> |
a rigid three-site model developed by Straub and Karplus for studying |
| 144 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 145 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 146 |
|
|
| 152 |
|
methods,\cite{Daw84,Foiles86,Johnson89,Daw89,Plimpton93,Voter95a,Lu97,Alemany98} |
| 153 |
|
but other models like the Finnis-Sinclair\cite{Finnis84,Chen90} and |
| 154 |
|
the quantum-corrected Sutton-Chen method\cite{QSC,Qi99} have simpler |
| 155 |
< |
parameter sets. The glue model of Ercolessi {\it et al}.\cite{Ercolessi88} is among the |
| 156 |
< |
fastest of these density functional approaches. In |
| 157 |
< |
all of these models, atoms are treated as a positively charged |
| 158 |
< |
core with a radially-decaying valence electron distribution. To |
| 159 |
< |
calculate the energy for embedding the core at a particular location, |
| 160 |
< |
the electron density due to the valence electrons at all of the other |
| 161 |
< |
atomic sites is computed at atom $i$'s location, |
| 155 |
> |
parameter sets. The glue model of Ercolessi {\it et |
| 156 |
> |
al}.\cite{Ercolessi88} is among the fastest of these density |
| 157 |
> |
functional approaches. In all of these models, atoms are treated as a |
| 158 |
> |
positively charged core with a radially-decaying valence electron |
| 159 |
> |
distribution. To calculate the energy for embedding the core at a |
| 160 |
> |
particular location, the electron density due to the valence electrons |
| 161 |
> |
at all of the other atomic sites is computed at atom $i$'s location, |
| 162 |
|
\begin{equation*} |
| 163 |
|
\bar{\rho}_i = \sum_{j\neq i} \rho_j(r_{ij}) |
| 164 |
|
\end{equation*} |
| 189 |
|
melting,\cite{Belonoshko00,sankaranarayanan:155441,Sankaranarayanan:2005lr} |
| 190 |
|
fracture,\cite{Shastry:1996qg,Shastry:1998dx,mishin01:cu} crack |
| 191 |
|
propagation,\cite{BECQUART:1993rg,Rifkin1992} and alloying |
| 192 |
< |
dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} One of EAM's strengths |
| 193 |
< |
is its sensitivity to small changes in structure. This arises |
| 194 |
< |
because interactions |
| 195 |
< |
up to the third nearest neighbor were taken into account in the parameterization.\cite{Voter95a} |
| 196 |
< |
Comparing that to the glue model of Ercolessi {\it et al}.\cite{Ercolessi88} |
| 197 |
< |
which is only parameterized up to the nearest-neighbor |
| 198 |
< |
interactions, EAM is a suitable choice for systems where |
| 199 |
< |
the bulk properties are of secondary importance to low-index |
| 200 |
< |
surface structures. Additionally, the similarity of EAM's functional |
| 201 |
< |
treatment of the embedding energy to standard density functional |
| 202 |
< |
theory (DFT) makes fitting DFT-derived cross potentials with adsorbates somewhat easier. |
| 192 |
> |
dynamics.\cite{Shibata:2002hh,mishin02:b2nial,zope03:tial_ap,mishin05:phase_fe_ni} |
| 193 |
> |
One of EAM's strengths is its sensitivity to small changes in |
| 194 |
> |
structure. This is due to the inclusion of up to the third nearest |
| 195 |
> |
neighbor interactions during fitting of the parameters.\cite{Voter95a} |
| 196 |
> |
In comparison, the glue model of Ercolessi {\it et |
| 197 |
> |
al}.\cite{Ercolessi88} was only parameterized to include |
| 198 |
> |
nearest-neighbor interactions, EAM is a suitable choice for systems |
| 199 |
> |
where the bulk properties are of secondary importance to low-index |
| 200 |
> |
surface structures. Additionally, the similarity of EAM's functional |
| 201 |
> |
treatment of the embedding energy to standard density functional |
| 202 |
> |
theory (DFT) makes fitting DFT-derived cross potentials with |
| 203 |
> |
adsorbates somewhat easier. |
| 204 |
|
|
| 228 |
– |
|
| 229 |
– |
|
| 230 |
– |
|
| 231 |
– |
|
| 205 |
|
\subsection{Carbon Monoxide model} |
| 206 |
< |
Previous explanations for the surface rearrangements center on |
| 207 |
< |
the large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} |
| 208 |
< |
We used a model first proposed by Karplus and Straub to study |
| 209 |
< |
the photodissociation of CO from myoglobin because it reproduces |
| 210 |
< |
the quadrupole moment well.\cite{Straub} The Straub and |
| 211 |
< |
Karplus model treats CO as a rigid three site molecule with a massless M |
| 212 |
< |
site at the molecular center of mass. The geometry and interaction |
| 213 |
< |
parameters are reproduced in Table~\ref{tab:CO}. The effective |
| 214 |
< |
dipole moment, calculated from the assigned charges, is still |
| 215 |
< |
small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is close |
| 216 |
< |
to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 206 |
> |
Previous explanations for the surface rearrangements center on the |
| 207 |
> |
large linear quadrupole moment of carbon monoxide.\cite{Tao:2010} We |
| 208 |
> |
used a model first proposed by Karplus and Straub to study the |
| 209 |
> |
photodissociation of CO from myoglobin because it reproduces the |
| 210 |
> |
quadrupole moment well.\cite{Straub} The Straub and Karplus model |
| 211 |
> |
treats CO as a rigid three site molecule with a massless |
| 212 |
> |
charge-carrying ``M'' site at the center of mass. The geometry and |
| 213 |
> |
interaction parameters are reproduced in Table~\ref{tab:CO}. The |
| 214 |
> |
effective dipole moment, calculated from the assigned charges, is |
| 215 |
> |
still small (0.35 D) while the linear quadrupole (-2.40 D~\AA) is |
| 216 |
> |
close to the experimental (-2.63 D~\AA)\cite{QuadrupoleCO} and quantum |
| 217 |
|
mechanical predictions (-2.46 D~\AA)\cite{QuadrupoleCOCalc}. |
| 218 |
|
%CO Table |
| 219 |
|
\begin{table}[H] |
| 220 |
|
\caption{Positions, Lennard-Jones parameters ($\sigma$ and |
| 221 |
< |
$\epsilon$), and charges for the CO-CO |
| 222 |
< |
interactions in Ref.\bibpunct{}{}{,}{n}{}{,} \protect\cite{Straub}. Distances are in \AA, energies are |
| 223 |
< |
in kcal/mol, and charges are in atomic units.} |
| 221 |
> |
$\epsilon$), and charges for CO-CO |
| 222 |
> |
interactions. Distances are in \AA, energies are |
| 223 |
> |
in kcal/mol, and charges are in atomic units. The CO model |
| 224 |
> |
from Ref.\bibpunct{}{}{,}{n}{}{,} |
| 225 |
> |
\protect\cite{Straub} was used without modification.} |
| 226 |
|
\centering |
| 227 |
|
\begin{tabular}{| c | c | ccc |} |
| 228 |
|
\hline |
| 268 |
|
The limited experimental data for CO adsorption on Au required refining the fits against plane-wave DFT calculations. |
| 269 |
|
Adsorption energies were obtained from gas-surface DFT calculations with a |
| 270 |
|
periodic supercell plane-wave basis approach, as implemented in the |
| 271 |
< |
{\sc Quantum ESPRESSO} package.\cite{QE-2009} Electron cores were |
| 271 |
> |
Quantum ESPRESSO package.\cite{QE-2009} Electron cores were |
| 272 |
|
described with the projector augmented-wave (PAW) |
| 273 |
|
method,\cite{PhysRevB.50.17953,PhysRevB.59.1758} with plane waves |
| 274 |
|
included to an energy cutoff of 20 Ry. Electronic energies are |
| 292 |
|
are shown in Table~\ref{tab:co_parameters} and the binding energies on the |
| 293 |
|
(111) surfaces are displayed in Table~\ref{tab:co_energies}. Charge transfer |
| 294 |
|
and polarization are neglected in this model, although these effects could have |
| 295 |
< |
an effect on binding energies and binding site preferences. |
| 295 |
> |
an effect on binding energies and binding site preferences. |
| 296 |
|
|
| 297 |
|
%Table of Parameters |
| 298 |
|
%Pt Parameter Set 9 |
| 299 |
|
%Au Parameter Set 35 |
| 300 |
|
\begin{table}[H] |
| 301 |
< |
\caption{Best fit parameters for metal-CO cross-interactions. Metal-C |
| 302 |
< |
interactions are modeled with Lennard-Jones potentials. While the |
| 303 |
< |
metal-O interactions were fit to Morse |
| 301 |
> |
\caption{Parameters for the metal-CO cross-interactions. Metal-C |
| 302 |
> |
interactions are modeled with Lennard-Jones potentials, while the |
| 303 |
> |
metal-O interactions were fit to broad Morse |
| 304 |
|
potentials. Distances are given in \AA~and energies in kcal/mol. } |
| 305 |
|
\centering |
| 306 |
|
\begin{tabular}{| c | cc | c | ccc |} |
| 324 |
|
\hline |
| 325 |
|
& Calculated & Experimental \\ |
| 326 |
|
\hline |
| 327 |
< |
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.9} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
| 327 |
> |
\multirow{2}{*}{\textbf{Pt-CO}} & \multirow{2}{*}{-1.84} & -1.4 \bibpunct{}{}{,}{n}{}{,} |
| 328 |
|
(Ref. \protect\cite{Kelemen:1979}) \\ |
| 329 |
|
& & -1.9 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{Yeo}) \\ \hline |
| 330 |
|
\textbf{Au-CO} & -0.39 & -0.40 \bibpunct{}{}{,}{n}{}{,} (Ref. \protect\cite{TPDGold}) \\ |
| 333 |
|
\label{tab:co_energies} |
| 334 |
|
\end{table} |
| 335 |
|
|
| 336 |
+ |
|
| 337 |
+ |
\subsection{Forcefield validation} |
| 338 |
+ |
The CO-metal cross interactions were compared directly to DFT results |
| 339 |
+ |
found in the supporting information of Tao {\it et al.} |
| 340 |
+ |
\cite{Tao:2010} These calculations are estimates of the stabilization |
| 341 |
+ |
energy provided to double-layer reconstructions of the perfect 557 |
| 342 |
+ |
surface by an overlayer of CO molecules in a $c (2 \times 4)$ pattern. |
| 343 |
+ |
To make the comparison, metal slabs that were five atoms thick and |
| 344 |
+ |
which displayed a 557 facet were constructed. Double-layer |
| 345 |
+ |
(reconstructed) systems were created using six atomic layers where |
| 346 |
+ |
enough of a layer was removed from both exposed 557 facets to create |
| 347 |
+ |
the double step. In all cases, the metal slabs contained 480 atoms |
| 348 |
+ |
and were minimized using steepest descent under the EAM force |
| 349 |
+ |
field. Both the bare metal slabs and slabs with 50\% carbon monoxide |
| 350 |
+ |
coverage (arranged in the $c (2 \times 4)$ pattern) were used. The |
| 351 |
+ |
systems are periodic along and perpendicular to the step-edge axes |
| 352 |
+ |
with a large vacuum above the displayed 557 facet. |
| 353 |
+ |
|
| 354 |
+ |
Energies using our force field for the various systems are displayed |
| 355 |
+ |
in Table ~\ref{tab:steps}. The relative energies are calculated as |
| 356 |
+ |
$E_{relative} = E_{system} - E_{M-557-S} - N_{CO} E_{CO-M}$, |
| 357 |
+ |
where $E_{CO-M}$ is -1.84 eV for CO-Pt and -0.39 eV for CO-Au. For |
| 358 |
+ |
platinum, the bare double layer is slightly less stable then the |
| 359 |
+ |
original single (557) step. However, addition of carbon monoxide |
| 360 |
+ |
stabilizes the reconstructed double layer relative to the perfect 557. |
| 361 |
+ |
This result is in qualitative agreement with DFT calculations in Tao |
| 362 |
+ |
{\it et al.}\cite{Tao:2010}, who also showed that the addition of CO |
| 363 |
+ |
leads to a reversal in stability. |
| 364 |
+ |
|
| 365 |
+ |
The DFT calculations suggest an increased stability of 0.08 kcal/mol |
| 366 |
+ |
(0.7128 eV) per Pt atom for going from the single to double step |
| 367 |
+ |
structure in the presence of carbon monoxide. |
| 368 |
+ |
|
| 369 |
+ |
The gold systems show much smaller energy differences between the |
| 370 |
+ |
single and double layers. The weaker binding of CO to Au is evidenced |
| 371 |
+ |
by the much smaller change in relative energy between the structures |
| 372 |
+ |
when carbon monoxide is present. Additionally, as CO-Au binding is |
| 373 |
+ |
much weaker than CO-Pt, it would be unlikely that CO would approach |
| 374 |
+ |
the 50\% coverage levels operating temperatures for the gold surfaces. |
| 375 |
+ |
|
| 376 |
+ |
%Table of single step double step calculations |
| 377 |
+ |
\begin{table}[H] |
| 378 |
+ |
\caption{Minimized single point energies of (S)ingle and (D)ouble |
| 379 |
+ |
steps. The addition of CO in a 50\% $c(2 \times 4)$ coverage acts as a |
| 380 |
+ |
stabilizing presence and suggests a driving force for the observed |
| 381 |
+ |
reconstruction on the highest coverage Pt system. All energies are |
| 382 |
+ |
in kcal/mol.} |
| 383 |
+ |
\centering |
| 384 |
+ |
\begin{tabular}{| c | c | c | c | c | c |} |
| 385 |
+ |
\hline |
| 386 |
+ |
\textbf{Step} & \textbf{N}\textsubscript{M} & \textbf{N\textsubscript{CO}} & \textbf{Relative Energy} & \textbf{$\Delta$E/M} & \textbf{$\Delta$E/CO} \\ |
| 387 |
+ |
\hline |
| 388 |
+ |
Pt(557)-S & 480 & 0 & 0 & 0 & - \\ |
| 389 |
+ |
Pt(557)-D & 480 & 0 & 114.783 & 0.239 & -\\ |
| 390 |
+ |
Pt(557)-S & 480 & 40 & -124.546 & -0.259 & -3.114\\ |
| 391 |
+ |
Pt(557)-D & 480 & 44 & -34.953 & -0.073 & -0.794\\ |
| 392 |
+ |
\hline |
| 393 |
+ |
\hline |
| 394 |
+ |
Au(557)-S & 480 & 0 & 0 & 0 & - \\ |
| 395 |
+ |
Au(557)-D & 480 & 0 & 79.572 & 0.166 & - \\ |
| 396 |
+ |
Au(557)-S & 480 & 40 & -157.199 & -0.327 & -3.930\\ |
| 397 |
+ |
Au(557)-D & 480 & 44 & -123.297 & -0.257 & -2.802 \\ |
| 398 |
+ |
\hline |
| 399 |
+ |
\end{tabular} |
| 400 |
+ |
\label{tab:steps} |
| 401 |
+ |
\end{table} |
| 402 |
+ |
|
| 403 |
+ |
|
| 404 |
|
\subsection{Pt(557) and Au(557) metal interfaces} |
| 405 |
|
Our Pt system is an orthorhombic periodic box of dimensions |
| 406 |
|
54.482~x~50.046~x~120.88~\AA~while our Au system has |
| 415 |
|
1200~K were performed to confirm the relative |
| 416 |
|
stability of the surfaces without a CO overlayer. |
| 417 |
|
|
| 418 |
< |
The different bulk melting temperatures predicted by EAM (1345~$\pm$~10~K for Au\cite{Au:melting} |
| 419 |
< |
and $\sim$~2045~K for Pt\cite{Pt:melting}) suggest that any possible reconstruction should happen at |
| 420 |
< |
different temperatures for the two metals. The bare Au and Pt surfaces were |
| 421 |
< |
initially run in the canonical (NVT) ensemble at 800~K and 1000~K |
| 422 |
< |
respectively for 100 ps. The two surfaces were relatively stable at these |
| 423 |
< |
temperatures when no CO was present, but experienced increased surface |
| 424 |
< |
mobility on addition of CO. Each surface was then dosed with different concentrations of CO |
| 425 |
< |
that was initially placed in the vacuum region. Upon full adsorption, |
| 426 |
< |
these concentrations correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface |
| 427 |
< |
coverage. Higher coverages resulted in the formation of a double layer of CO, |
| 428 |
< |
which introduces artifacts that are not relevant to (557) reconstruction. |
| 429 |
< |
Because of the difference in binding energies, nearly all of the CO was bound to the Pt surface, while |
| 430 |
< |
the Au surfaces often had a significant CO population in the gas |
| 431 |
< |
phase. These systems were allowed to reach thermal equilibrium (over |
| 432 |
< |
5~ns) before being run in the microcanonical (NVE) ensemble for |
| 433 |
< |
data collection. All of the systems examined had at least 40~ns in the |
| 434 |
< |
data collection stage, although simulation times for some Pt of the |
| 435 |
< |
systems exceeded 200~ns. Simulations were carried out using the open |
| 436 |
< |
source molecular dynamics package, OpenMD.\cite{Ewald,OOPSE,openmd} |
| 418 |
> |
The different bulk melting temperatures predicted by EAM |
| 419 |
> |
(1345~$\pm$~10~K for Au\cite{Au:melting} and $\sim$~2045~K for |
| 420 |
> |
Pt\cite{Pt:melting}) suggest that any reconstructions should happen at |
| 421 |
> |
different temperatures for the two metals. The bare Au and Pt |
| 422 |
> |
surfaces were initially run in the canonical (NVT) ensemble at 800~K |
| 423 |
> |
and 1000~K respectively for 100 ps. The two surfaces were relatively |
| 424 |
> |
stable at these temperatures when no CO was present, but experienced |
| 425 |
> |
increased surface mobility on addition of CO. Each surface was then |
| 426 |
> |
dosed with different concentrations of CO that was initially placed in |
| 427 |
> |
the vacuum region. Upon full adsorption, these concentrations |
| 428 |
> |
correspond to 0\%, 5\%, 25\%, 33\%, and 50\% surface coverage. Higher |
| 429 |
> |
coverages resulted in the formation of a double layer of CO, which |
| 430 |
> |
introduces artifacts that are not relevant to (557) reconstruction. |
| 431 |
> |
Because of the difference in binding energies, nearly all of the CO |
| 432 |
> |
was bound to the Pt surface, while the Au surfaces often had a |
| 433 |
> |
significant CO population in the gas phase. These systems were |
| 434 |
> |
allowed to reach thermal equilibrium (over 5~ns) before being run in |
| 435 |
> |
the microcanonical (NVE) ensemble for data collection. All of the |
| 436 |
> |
systems examined had at least 40~ns in the data collection stage, |
| 437 |
> |
although simulation times for some Pt of the systems exceeded 200~ns. |
| 438 |
> |
Simulations were carried out using the open source molecular dynamics |
| 439 |
> |
package, OpenMD.\cite{Ewald,OOPSE,openmd} |
| 440 |
|
|
| 441 |
|
|
| 396 |
– |
|
| 397 |
– |
|
| 442 |
|
% RESULTS |
| 443 |
|
% |
| 444 |
|
\section{Results} |
| 445 |
|
\subsection{Structural remodeling} |
| 446 |
< |
The bare metal surfaces experienced minor roughening of the |
| 447 |
< |
step-edge because of the elevated temperatures, but the (557) |
| 448 |
< |
face was stable throughout the simulations. The surface of both |
| 449 |
< |
systems, upon dosage of CO, began to undergo extensive remodeling |
| 450 |
< |
that was not observed in the bare systems. Reconstructions of |
| 451 |
< |
the Au systems were limited to breakup of the step-edges and |
| 452 |
< |
some step wandering. The lower coverage Pt systems experienced |
| 453 |
< |
similar restructuring but to a greater extent. The 50\% coverage |
| 454 |
< |
Pt system was unique among our simulations in that it formed |
| 455 |
< |
well-defined and stable double layers through step coalescence, |
| 456 |
< |
similar to results reported by Tao {\it et al}.\cite{Tao:2010} |
| 413 |
< |
|
| 414 |
< |
|
| 415 |
< |
\subsubsection{Step wandering} |
| 416 |
< |
The 0\% coverage surfaces for both metals showed minimal |
| 417 |
< |
step-wandering at their respective temperatures. As the CO |
| 418 |
< |
coverage increased however, the mobility of the surface atoms, |
| 419 |
< |
described through adatom diffusion and step-edge wandering, |
| 420 |
< |
also increased. Except for the 50\% Pt system where step |
| 421 |
< |
coalescence occurred, the step-edges in the other simulations |
| 422 |
< |
preferred to keep nearly the same distance between steps as in |
| 423 |
< |
the original (557) lattice, $\sim$13\AA~for Pt and $\sim$14\AA~for Au. |
| 424 |
< |
Previous work by Williams {\it 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 is caused by an entropic barrier that arises from |
| 428 |
< |
the fact that steps cannot cross over one another. This entropic |
| 429 |
< |
repulsion does not completely define the interactions between |
| 430 |
< |
steps, however, so it is possible to observe step coalescence |
| 431 |
< |
on some surfaces.\cite{Williams:1991} The presence and |
| 432 |
< |
concentration of adsorbates, as shown in this work, can |
| 433 |
< |
affect step-step interactions, potentially leading to a new |
| 434 |
< |
surface structure as the thermodynamic equilibrium. |
| 446 |
> |
The bare metal surfaces experienced minor roughening of the step-edge |
| 447 |
> |
because of the elevated temperatures, but the (557) face was stable |
| 448 |
> |
throughout the simulations. The surfaces of both systems, upon dosage |
| 449 |
> |
of CO, began to undergo extensive remodeling that was not observed in |
| 450 |
> |
the bare systems. Reconstructions of the Au systems were limited to |
| 451 |
> |
breakup of the step-edges and some step wandering. The lower coverage |
| 452 |
> |
Pt systems experienced similar step edge wandering but to a greater |
| 453 |
> |
extent. The 50\% coverage Pt system was unique among our simulations |
| 454 |
> |
in that it formed well-defined and stable double layers through step |
| 455 |
> |
coalescence, similar to results reported by Tao {\it et |
| 456 |
> |
al}.\cite{Tao:2010} |
| 457 |
|
|
| 458 |
+ |
\subsubsection{Step wandering} |
| 459 |
+ |
The bare surfaces for both metals showed minimal step-wandering at |
| 460 |
+ |
their respective temperatures. As the CO coverage increased however, |
| 461 |
+ |
the mobility of the surface atoms, described through adatom diffusion |
| 462 |
+ |
and step-edge wandering, also increased. Except for the 50\% Pt |
| 463 |
+ |
system where step coalescence occurred, the step-edges in the other |
| 464 |
+ |
simulations preferred to keep nearly the same distance between steps |
| 465 |
+ |
as in the original (557) lattice, $\sim$13\AA~for Pt and |
| 466 |
+ |
$\sim$14\AA~for Au. Previous work by Williams {\it et |
| 467 |
+ |
al}.\cite{Williams:1991, Williams:1994} highlights the repulsion |
| 468 |
+ |
that exists between step-edges even when no direct interactions are |
| 469 |
+ |
present in the system. This repulsion is caused by an entropic barrier |
| 470 |
+ |
that arises from the fact that steps cannot cross over one |
| 471 |
+ |
another. This entropic repulsion does not completely define the |
| 472 |
+ |
interactions between steps, however, so it is possible to observe step |
| 473 |
+ |
coalescence on some surfaces.\cite{Williams:1991} The presence and |
| 474 |
+ |
concentration of adsorbates, as shown in this work, can affect |
| 475 |
+ |
step-step interactions, potentially leading to a new surface structure |
| 476 |
+ |
as the thermodynamic equilibrium. |
| 477 |
+ |
|
| 478 |
|
\subsubsection{Double layers} |
| 479 |
< |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the Pt(557) surface |
| 480 |
< |
undergoes two separate reconstructions upon CO adsorption. |
| 481 |
< |
The first involves a doubling of the step height and plateau length. |
| 482 |
< |
Similar behavior has been seen on a number of surfaces |
| 483 |
< |
at varying conditions, including Ni(977) and Si(111).\cite{Williams:1994,Williams:1991,Pearl} |
| 484 |
< |
Of the two systems we examined, the Pt system showed a greater |
| 485 |
< |
propensity for reconstruction |
| 486 |
< |
because of the larger surface mobility and the greater extent of step wandering. |
| 487 |
< |
The amount of reconstruction was strongly correlated to the amount of CO |
| 488 |
< |
adsorbed upon the surface. This appears to be related to the |
| 489 |
< |
effect that adsorbate coverage has on edge breakup and on the |
| 490 |
< |
surface diffusion of metal adatoms. Only the 50\% Pt surface underwent the |
| 491 |
< |
doubling seen by Tao {\it et al}.\cite{Tao:2010} within the time scales studied here. |
| 492 |
< |
Over a longer time scale (150~ns) two more double layers formed |
| 493 |
< |
on this surface. Although double layer formation did not occur |
| 494 |
< |
in the other Pt systems, they exhibited more step-wandering and |
| 495 |
< |
roughening compared to their Au counterparts. The |
| 496 |
< |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 497 |
< |
various times along the simulation showing the evolution of a double layer step-edge. |
| 479 |
> |
Tao {\it et al}.\cite{Tao:2010} have shown experimentally that the |
| 480 |
> |
Pt(557) surface undergoes two separate reconstructions upon CO |
| 481 |
> |
adsorption. The first involves a doubling of the step height and |
| 482 |
> |
plateau length. Similar behavior has been seen on a number of |
| 483 |
> |
surfaces at varying conditions, including Ni(977) and |
| 484 |
> |
Si(111).\cite{Williams:1994,Williams:1991,Pearl} Of the two systems we |
| 485 |
> |
examined, the Pt system showed a greater propensity for reconstruction |
| 486 |
> |
because of the larger surface mobility and the greater extent of step |
| 487 |
> |
wandering. The amount of reconstruction was strongly correlated to |
| 488 |
> |
the amount of CO adsorbed upon the surface. This appears to be |
| 489 |
> |
related to the effect that adsorbate coverage has on edge breakup and |
| 490 |
> |
on the surface diffusion of metal adatoms. Only the 50\% Pt surface |
| 491 |
> |
underwent the doubling seen by Tao {\it et al}.\cite{Tao:2010} within |
| 492 |
> |
the time scales studied here. Over a longer time scale (150~ns) two |
| 493 |
> |
more double layers formed on this surface. Although double layer |
| 494 |
> |
formation did not occur in the other Pt systems, they exhibited more |
| 495 |
> |
step-wandering and roughening compared to their Au counterparts. The |
| 496 |
> |
50\% Pt system is highlighted in Figure \ref{fig:reconstruct} at |
| 497 |
> |
various times along the simulation showing the evolution of a double |
| 498 |
> |
layer step-edge. |
| 499 |
|
|
| 500 |
< |
The second reconstruction observed by |
| 501 |
< |
Tao {\it et al}.\cite{Tao:2010} involved the formation of triangular clusters that stretched |
| 502 |
< |
across the plateau between two step-edges. Neither metal, within |
| 503 |
< |
the 40~ns time scale or the extended simulation time of 150~ns for |
| 504 |
< |
the 50\% Pt system, experienced this reconstruction. |
| 500 |
> |
The second reconstruction observed by Tao {\it et al}.\cite{Tao:2010} |
| 501 |
> |
involved the formation of triangular clusters that stretched across |
| 502 |
> |
the plateau between two step-edges. Neither of the simulated metal |
| 503 |
> |
interfaces, within the 40~ns time scale or the extended time of 150~ns |
| 504 |
> |
for the 50\% Pt system, experienced this reconstruction. |
| 505 |
|
|
| 506 |
|
%Evolution of surface |
| 507 |
|
\begin{figure}[H] |
| 508 |
|
\includegraphics[width=\linewidth]{EPS_ProgressionOfDoubleLayerFormation} |
| 509 |
< |
\caption{The Pt(557) / 50\% CO system at a sequence of times after |
| 510 |
< |
initial exposure to the CO: (a) 258~ps, (b) 19~ns, (c) 31.2~ns, and |
| 511 |
< |
(d) 86.1~ns. Disruption of the (557) step-edges occurs quickly. The |
| 509 |
> |
\caption{The Pt(557) / 50\% CO interface upon exposure to the CO: (a) |
| 510 |
> |
258~ps, (b) 19~ns, (c) 31.2~ns, and (d) 86.1~ns after |
| 511 |
> |
exposure. Disruption of the (557) step-edges occurs quickly. The |
| 512 |
|
doubling of the layers appears only after two adjacent step-edges |
| 513 |
|
touch. The circled spot in (b) nucleated the growth of the double |
| 514 |
|
step observed in the later configurations.} |
| 516 |
|
\end{figure} |
| 517 |
|
|
| 518 |
|
\subsection{Dynamics} |
| 519 |
< |
Previous experimental work by Pearl and Sibener\cite{Pearl}, |
| 520 |
< |
using STM, has been able to capture the coalescence of steps |
| 521 |
< |
on Ni(977). The time scale of the image acquisition, $\sim$70~s/image, |
| 522 |
< |
provides an upper bound for the time required for the doubling |
| 523 |
< |
to occur. By utilizing Molecular Dynamics we are able to probe |
| 524 |
< |
the dynamics of these reconstructions at elevated temperatures |
| 525 |
< |
and in this section we provide data on the timescales for transport |
| 526 |
< |
properties, e.g. diffusion and layer formation time. |
| 519 |
> |
Previous experimental work by Pearl and Sibener\cite{Pearl}, using |
| 520 |
> |
STM, has been able to capture the coalescence of steps on Ni(977). The |
| 521 |
> |
time scale of the image acquisition, $\sim$70~s/image, provides an |
| 522 |
> |
upper bound for the time required for the doubling to occur. By |
| 523 |
> |
utilizing Molecular Dynamics we are able to probe the dynamics of |
| 524 |
> |
these reconstructions at elevated temperatures and in this section we |
| 525 |
> |
provide data on the timescales for transport properties, |
| 526 |
> |
e.g. diffusion and layer formation time. |
| 527 |
|
|
| 528 |
|
|
| 529 |
|
\subsubsection{Transport of surface metal atoms} |
| 530 |
|
%forcedSystems/stepSeparation |
| 488 |
– |
The wandering of a step-edge is a cooperative effect |
| 489 |
– |
arising from the individual movements of the atoms making up the steps. An ideal metal surface |
| 490 |
– |
displaying a low index facet, (111) or (100), is unlikely to experience |
| 491 |
– |
much surface diffusion because of the large energetic barrier that must |
| 492 |
– |
be overcome to lift an atom out of the surface. The presence of step-edges and other surface features |
| 493 |
– |
on higher-index facets provides a lower energy source for mobile metal atoms. |
| 494 |
– |
Single-atom break-away from a step-edge on a clean surface still imposes an |
| 495 |
– |
energetic penalty around $\sim$~45 kcal/mol, but this is easier than lifting |
| 496 |
– |
the same metal atom vertically out of the surface, \textgreater~60 kcal/mol. |
| 497 |
– |
The penalty lowers significantly when CO is present in sufficient quantities |
| 498 |
– |
on the surface. For certain distributions of CO, see Discussion, the penalty can fall to as low as |
| 499 |
– |
$\sim$~20 kcal/mol. Once an adatom exists on the surface, the barrier for |
| 500 |
– |
diffusion is negligible (\textless~4 kcal/mol for a Pt adatom). These adatoms are then |
| 501 |
– |
able to explore the terrace before rejoining either their original step-edge or |
| 502 |
– |
becoming a part of a different edge. It is an energetically unfavorable process with a high barrier for an atom |
| 503 |
– |
to traverse to a separate terrace although the presence of CO can lower the |
| 504 |
– |
energy barrier required to lift or lower an adatom. By tracking the mobility of individual |
| 505 |
– |
metal atoms on the Pt and Au surfaces we were able to determine the relative |
| 506 |
– |
diffusion constants, as well as how varying coverages of CO affect the diffusion. Close |
| 507 |
– |
observation of the mobile metal atoms showed that they were typically in |
| 508 |
– |
equilibrium with the step-edges. |
| 509 |
– |
At times, their motion was concerted and two or more adatoms would be |
| 510 |
– |
observed moving together across the surfaces. |
| 531 |
|
|
| 532 |
< |
A particle was considered ``mobile'' once it had traveled more than 2~\AA~ |
| 533 |
< |
between saved configurations of the system (typically 10-100 ps). A mobile atom |
| 534 |
< |
would typically travel much greater distances than this, but the 2~\AA~cutoff |
| 535 |
< |
was used to prevent swamping the diffusion data with the in-place vibrational |
| 536 |
< |
movement of buried atoms. Diffusion on a surface is strongly affected by |
| 537 |
< |
local structures and in this work, the presence of single and double layer |
| 538 |
< |
step-edges causes the diffusion parallel to the step-edges to be larger than |
| 539 |
< |
the diffusion perpendicular to these edges. Parallel and perpendicular |
| 540 |
< |
diffusion constants are shown in Figure \ref{fig:diff}. |
| 532 |
> |
The wandering of a step-edge is a cooperative effect arising from the |
| 533 |
> |
individual movements of the atoms making up the steps. An ideal metal |
| 534 |
> |
surface displaying a low index facet, (111) or (100), is unlikely to |
| 535 |
> |
experience much surface diffusion because of the large energetic |
| 536 |
> |
barrier that must be overcome to lift an atom out of the surface. The |
| 537 |
> |
presence of step-edges and other surface features on higher-index |
| 538 |
> |
facets provides a lower energy source for mobile metal atoms. Using |
| 539 |
> |
our potential model, single-atom break-away from a step-edge on a |
| 540 |
> |
clean surface still imposes an energetic penalty around |
| 541 |
> |
$\sim$~45~kcal/mol, but this is certainly easier than lifting the same |
| 542 |
> |
metal atom vertically out of the surface, \textgreater~60~kcal/mol. |
| 543 |
> |
The penalty lowers significantly when CO is present in sufficient |
| 544 |
> |
quantities on the surface. For certain distributions of CO, the |
| 545 |
> |
energetic penalty can fall to as low as $\sim$~20~kcal/mol. The |
| 546 |
> |
configurations that create these lower barriers are detailed in the |
| 547 |
> |
discussion section below. |
| 548 |
> |
|
| 549 |
> |
Once an adatom exists on the surface, the barrier for diffusion is |
| 550 |
> |
negligible (\textless~4~kcal/mol for a Pt adatom). These adatoms are |
| 551 |
> |
then able to explore the terrace before rejoining either their |
| 552 |
> |
original step-edge or becoming a part of a different edge. It is an |
| 553 |
> |
energetically unfavorable process with a high barrier for an atom to |
| 554 |
> |
traverse to a separate terrace although the presence of CO can lower |
| 555 |
> |
the energy barrier required to lift or lower an adatom. By tracking |
| 556 |
> |
the mobility of individual metal atoms on the Pt and Au surfaces we |
| 557 |
> |
were able to determine the relative diffusion constants, as well as |
| 558 |
> |
how varying coverages of CO affect the diffusion. Close observation of |
| 559 |
> |
the mobile metal atoms showed that they were typically in equilibrium |
| 560 |
> |
with the step-edges. At times, their motion was concerted, and two or |
| 561 |
> |
more adatoms would be observed moving together across the surfaces. |
| 562 |
> |
|
| 563 |
> |
A particle was considered ``mobile'' once it had traveled more than |
| 564 |
> |
2~\AA~ between saved configurations of the system (typically 10-100 |
| 565 |
> |
ps). A mobile atom would typically travel much greater distances than |
| 566 |
> |
this, but the 2~\AA~cutoff was used to prevent swamping the diffusion |
| 567 |
> |
data with the in-place vibrational movement of buried atoms. Diffusion |
| 568 |
> |
on a surface is strongly affected by local structures and the presence |
| 569 |
> |
of single and double layer step-edges causes the diffusion parallel to |
| 570 |
> |
the step-edges to be larger than the diffusion perpendicular to these |
| 571 |
> |
edges. Parallel and perpendicular diffusion constants are shown in |
| 572 |
> |
Figure \ref{fig:diff}. Diffusion parallel to the step-edge is higher |
| 573 |
> |
than diffusion perpendicular to the edge because of the lower energy |
| 574 |
> |
barrier associated with sliding along an edge compared to breaking |
| 575 |
> |
away to form an isolated adatom. |
| 576 |
|
|
| 577 |
|
%Diffusion graph |
| 578 |
|
\begin{figure}[H] |
| 580 |
|
\caption{Diffusion constants for mobile surface atoms along directions |
| 581 |
|
parallel ($\mathbf{D}_{\parallel}$) and perpendicular |
| 582 |
|
($\mathbf{D}_{\perp}$) to the (557) step-edges as a function of CO |
| 583 |
< |
surface coverage. Diffusion parallel to the step-edge is higher |
| 584 |
< |
than that perpendicular to the edge because of the lower energy |
| 585 |
< |
barrier associated with traversing along the edge as compared to |
| 586 |
< |
completely breaking away. The two reported diffusion constants for |
| 532 |
< |
the 50\% Pt system arise from different sample sets. The lower values |
| 533 |
< |
correspond to the same 40~ns amount that all of the other systems were |
| 534 |
< |
examined at, while the larger values correspond to a 20~ns period } |
| 583 |
> |
surface coverage. The two reported diffusion constants for the 50\% |
| 584 |
> |
Pt system correspond to a 20~ns period before the formation of the |
| 585 |
> |
double layer (upper points), and to the full 40~ns sampling period |
| 586 |
> |
(lower points).} |
| 587 |
|
\label{fig:diff} |
| 588 |
|
\end{figure} |
| 589 |
|
|
| 595 |
|
at the earliest times in the simulations. Following double layer formation, |
| 596 |
|
however, there is a precipitous drop in adatom diffusion. As the double |
| 597 |
|
layer forms, many atoms that had been tracked for mobility data have |
| 598 |
< |
now been buried resulting in a smaller reported diffusion constant. A |
| 598 |
> |
now been buried, resulting in a smaller reported diffusion constant. A |
| 599 |
|
secondary effect of higher coverages is CO-CO cross interactions that |
| 600 |
|
lower the effective mobility of the Pt adatoms that are bound to each CO. |
| 601 |
|
This effect would become evident only at higher coverages. A detailed |
| 602 |
|
account of Pt adatom energetics follows in the Discussion. |
| 603 |
|
|
| 552 |
– |
|
| 604 |
|
\subsubsection{Dynamics of double layer formation} |
| 605 |
|
The increased diffusion on Pt at the higher CO coverages is the primary |
| 606 |
|
contributor to double layer formation. However, this is not a complete |
| 660 |
|
possibility. However, the quadrupole-quadrupole interaction is |
| 661 |
|
short-ranged and is attractive for some orientations. If the CO |
| 662 |
|
molecules are ``locked'' in a vertical orientation, through atop |
| 663 |
< |
adsorption for example, this explanation would gain credence. The |
| 664 |
< |
calculated energetic repulsion between two CO molecules located a |
| 665 |
< |
distance of 2.77~\AA~apart (nearest-neighbor distance of Pt) and both |
| 666 |
< |
in a vertical orientation, is 8.62 kcal/mol. Moving the CO to the |
| 667 |
< |
second nearest-neighbor distance of 4.8~\AA~drops the repulsion to |
| 668 |
< |
nearly 0. Allowing the CO to rotate away from a purely vertical |
| 669 |
< |
orientation also lowers the repulsion. When the carbons are locked at |
| 670 |
< |
a distance of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the |
| 671 |
< |
angle between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
| 663 |
> |
adsorption for example, this explanation would gain credence. Within |
| 664 |
> |
the framework of our classical potential, the calculated energetic |
| 665 |
> |
repulsion between two CO molecules located a distance of |
| 666 |
> |
2.77~\AA~apart (nearest-neighbor distance of Pt) and both in a |
| 667 |
> |
vertical orientation, is 8.62 kcal/mol. Moving the CO to the second |
| 668 |
> |
nearest-neighbor distance of 4.8~\AA~drops the repulsion to nearly |
| 669 |
> |
0. Allowing the CO to rotate away from a purely vertical orientation |
| 670 |
> |
also lowers the repulsion. When the carbons are locked at a distance |
| 671 |
> |
of 2.77~\AA, a minimum of 6.2 kcal/mol is reached when the angle |
| 672 |
> |
between the 2 CO is $\sim$24\textsuperscript{o}. The calculated |
| 673 |
|
barrier for surface diffusion of a Pt adatom is only 4 kcal/mol, so |
| 674 |
< |
repulsion between adjacent CO molecules bound to Pt could increase the |
| 675 |
< |
surface diffusion. However, the residence time of CO on Pt suggests |
| 676 |
< |
that the CO molecules are extremely mobile, with diffusion constants 40 |
| 677 |
< |
to 2500 times larger than surface Pt atoms. This mobility suggests |
| 678 |
< |
that the CO molecules jump between different Pt atoms throughout the |
| 679 |
< |
simulation, but can stay bound for significant periods of time. |
| 674 |
> |
repulsion between adjacent CO molecules bound to Pt could indeed |
| 675 |
> |
increase the surface diffusion. However, the residence time of CO on |
| 676 |
> |
Pt suggests that the CO molecules are extremely mobile, with diffusion |
| 677 |
> |
constants 40 to 2500 times larger than surface Pt atoms. This mobility |
| 678 |
> |
suggests that the CO molecules jump between different Pt atoms |
| 679 |
> |
throughout the simulation. However, they do stay bound to individual |
| 680 |
> |
Pt atoms for long enough to modify the local energy landscape for the |
| 681 |
> |
mobile adatoms. |
| 682 |
|
|
| 683 |
|
A different interpretation of the above mechanism which takes the |
| 684 |
|
large mobility of the CO into account, would be in the destabilization |
| 695 |
|
populations. The roughening is present to a lesser extent on surfaces |
| 696 |
|
with lower CO coverage (and even on the bare surfaces), although in |
| 697 |
|
these cases it is likely due to random fluctuations that squeeze out |
| 698 |
< |
step-edge atoms. Step-edge breakup by continuous single-atom |
| 699 |
< |
translations (as suggested by these energy curves) is probably a |
| 700 |
< |
worst-case scenario. Multistep mechanisms in which an adatom moves |
| 701 |
< |
laterally on the surface after being ejected would be more |
| 702 |
< |
energetically favorable. This would leave the adatom alongside the |
| 703 |
< |
ledge, providing it with 5 nearest neighbors. While fewer than the 7 |
| 704 |
< |
neighbors it had as part of the step-edge, it keeps more Pt neighbors |
| 705 |
< |
than the 3 an isolated adatom would have on the terrace. In this |
| 706 |
< |
proposed mechanism, the CO quadrupolar repulsion still plays a role in |
| 707 |
< |
the initial roughening of the step-edge, but not in any long-term |
| 708 |
< |
bonds with individual Pt atoms. Higher CO coverages create more |
| 698 |
> |
step-edge atoms. Step-edge breakup by direct single-atom translations |
| 699 |
> |
(as suggested by these energy curves) is probably a worst-case |
| 700 |
> |
scenario. Multistep mechanisms in which an adatom moves laterally on |
| 701 |
> |
the surface after being ejected would be more energetically favorable. |
| 702 |
> |
This would leave the adatom alongside the ledge, providing it with |
| 703 |
> |
five nearest neighbors. While fewer than the seven neighbors it had |
| 704 |
> |
as part of the step-edge, it keeps more Pt neighbors than the three |
| 705 |
> |
neighbors an isolated adatom has on the terrace. In this proposed |
| 706 |
> |
mechanism, the CO quadrupolar repulsion still plays a role in the |
| 707 |
> |
initial roughening of the step-edge, but not in any long-term bonds |
| 708 |
> |
with individual Pt atoms. Higher CO coverages create more |
| 709 |
|
opportunities for the crowded CO configurations shown in Figure |
| 710 |
|
\ref{fig:SketchGraphic}, and this is likely to cause an increased |
| 711 |
|
propensity for step-edge breakup. |
| 714 |
|
\begin{figure}[H] |
| 715 |
|
\includegraphics[width=\linewidth]{COpaths} |
| 716 |
|
\caption{Configurations used to investigate the mechanism of step-edge |
| 717 |
< |
breakup on Pt(557). In each case, the central (starred) atom is |
| 717 |
> |
breakup on Pt(557). In each case, the central (starred) atom was |
| 718 |
|
pulled directly across the surface away from the step edge. The Pt |
| 719 |
|
atoms on the upper terrace are colored dark grey, while those on the |
| 720 |
|
lower terrace are in white. In each of these configurations, some |
| 721 |
< |
number of the atoms (highlighted in blue) had a CO molecule bound in |
| 722 |
< |
a vertical atop position. The energies of these configurations as a |
| 721 |
> |
of the atoms (highlighted in blue) had CO molecules bound in the |
| 722 |
> |
vertical atop position. The energies of these configurations as a |
| 723 |
|
function of central atom displacement are displayed in Figure |
| 724 |
|
\ref{fig:SketchEnergies}.} |
| 725 |
|
\label{fig:SketchGraphic} |
| 731 |
|
\caption{Energies for displacing a single edge atom perpendicular to |
| 732 |
|
the step edge as a function of atomic displacement. Each of the |
| 733 |
|
energy curves corresponds to one of the labeled configurations in |
| 734 |
< |
Figure \ref{fig:SketchGraphic}, and are referenced to the |
| 735 |
< |
unperturbed step-edge. Certain arrangements of bound CO (notably |
| 736 |
< |
configurations g and h) can lower the energetic barrier for creating |
| 737 |
< |
an adatom relative to the bare surface (configuration a).} |
| 734 |
> |
Figure \ref{fig:SketchGraphic}, and the energies are referenced to |
| 735 |
> |
the unperturbed step-edge. Certain arrangements of bound CO |
| 736 |
> |
(notably configurations g and h) can lower the energetic barrier for |
| 737 |
> |
creating an adatom relative to the bare surface (configuration a).} |
| 738 |
|
\label{fig:SketchEnergies} |
| 739 |
|
\end{figure} |
| 740 |
|
|
| 749 |
|
displacement of Pt atoms at the step edge. Figure \ref{fig:lambda} |
| 750 |
|
shows four points along a reaction coordinate in which a CO-bound |
| 751 |
|
adatom along the step-edge ``burrows'' into the edge and displaces the |
| 752 |
< |
original edge atom onto the higher terrace. A number of events similar |
| 753 |
< |
to this mechanism were observed during the simulations. We predict an |
| 754 |
< |
energetic barrier of 20~kcal/mol for this process (in which the |
| 755 |
< |
displaced edge atom follows a curvilinear path into an adjacent 3-fold |
| 756 |
< |
hollow site). The barrier heights we obtain for this reaction |
| 752 |
> |
original edge atom onto the higher terrace. A number of events |
| 753 |
> |
similar to this mechanism were observed during the simulations. We |
| 754 |
> |
predict an energetic barrier of 20~kcal/mol for this process (in which |
| 755 |
> |
the displaced edge atom follows a curvilinear path into an adjacent |
| 756 |
> |
3-fold hollow site). The barrier heights we obtain for this reaction |
| 757 |
|
coordinate are approximate because the exact path is unknown, but the |
| 758 |
|
calculated energy barriers would be easily accessible at operating |
| 759 |
|
conditions. Additionally, this mechanism is exothermic, with a final |
| 760 |
|
energy 15~kcal/mol below the original $\lambda = 0$ configuration. |
| 761 |
|
When CO is not present and this reaction coordinate is followed, the |
| 762 |
< |
process is endothermic by 3~kcal/mol. The difference in the relative |
| 762 |
> |
process is endothermic by 3~kcal/mol. The difference in the relative |
| 763 |
|
energies for the $\lambda=0$ and $\lambda=1$ case when CO is present |
| 764 |
|
provides strong support for CO-mediated Pt-Pt interactions giving rise |
| 765 |
< |
to the doubling reconstruction. |
| 765 |
> |
to the doubling reconstruction. |
| 766 |
|
|
| 767 |
|
%lambda progression of Pt -> shoving its way into the step |
| 768 |
|
\begin{figure}[H] |
| 772 |
|
step edge and displaces an edge atom onto the upper terrace along a |
| 773 |
|
curvilinear path. The approximate barrier for the process is |
| 774 |
|
20~kcal/mol, and the complete process is exothermic by 15~kcal/mol |
| 775 |
< |
in the presence of CO, but is endothermic by 3~kcal/mol without.} |
| 775 |
> |
in the presence of CO, but is endothermic by 3~kcal/mol without CO.} |
| 776 |
|
\label{fig:lambda} |
| 777 |
|
\end{figure} |
| 778 |
|
|
| 780 |
|
the cooperation of at least two distinct processes. For complete |
| 781 |
|
doubling of a layer to occur there must be a breakup of one |
| 782 |
|
terrace. These atoms must then ``disappear'' from that terrace, either |
| 783 |
< |
by travelling to the terraces above of below their original levels. |
| 783 |
> |
by travelling to the terraces above or below their original levels. |
| 784 |
|
The presence of CO helps explain mechanisms for both of these |
| 785 |
|
situations. There must be sufficient breakage of the step-edge to |
| 786 |
|
increase the concentration of adatoms on the surface and these adatoms |
| 789 |
|
mechanisms working in concert lead to the formation of a double layer. |
| 790 |
|
|
| 791 |
|
\subsection{CO Removal and double layer stability} |
| 792 |
< |
Once a double layer had formed on the 50\%~Pt system, it remained for |
| 793 |
< |
the rest of the simulation time with minimal movement. Random |
| 794 |
< |
fluctuations that involved small clusters or divots were observed, but |
| 795 |
< |
these features typically healed within a few nanoseconds. Within our |
| 796 |
< |
simulations, the formation of the double layer appeared to be |
| 797 |
< |
irreversible and a double layer was never observed to split back into |
| 798 |
< |
two single layer step-edges while CO was present. |
| 792 |
> |
Once the double layers had formed on the 50\%~Pt system, they remained |
| 793 |
> |
stable for the rest of the simulation time with minimal movement. |
| 794 |
> |
Random fluctuations that involved small clusters or divots were |
| 795 |
> |
observed, but these features typically healed within a few |
| 796 |
> |
nanoseconds. Within our simulations, the formation of the double |
| 797 |
> |
layer appeared to be irreversible and a double layer was never |
| 798 |
> |
observed to split back into two single layer step-edges while CO was |
| 799 |
> |
present. |
| 800 |
|
|
| 801 |
|
To further gauge the effect CO has on this surface, additional |
| 802 |
|
simulations were run starting from a late configuration of the 50\%~Pt |
| 803 |
|
system that had already formed double layers. These simulations then |
| 804 |
< |
had their CO forcibly removed. The double layer broke apart rapidly |
| 805 |
< |
in these simulations, showing a well-defined edge-splitting after |
| 806 |
< |
100~ps. Configurations of this system are shown in Figure |
| 804 |
> |
had their CO molecules suddenly removed. The double layer broke apart |
| 805 |
> |
rapidly in these simulations, showing a well-defined edge-splitting |
| 806 |
> |
after 100~ps. Configurations of this system are shown in Figure |
| 807 |
|
\ref{fig:breaking}. The coloring of the top and bottom layers helps to |
| 808 |
< |
exhibit how much mixing the edges experience as they split. These |
| 809 |
< |
systems were only examined for 10~ns, and within that time despite the |
| 810 |
< |
initial rapid splitting, the edges only moved another few |
| 811 |
< |
\AA~apart. It is possible that with longer simulation times, the (557) |
| 812 |
< |
surface recovery observed by Tao {\it et al}.\cite{Tao:2010} could |
| 758 |
< |
also be recovered. |
| 808 |
> |
show how much mixing the edges experience as they split. These systems |
| 809 |
> |
were only examined for 10~ns, and within that time despite the initial |
| 810 |
> |
rapid splitting, the edges only moved another few \AA~apart. It is |
| 811 |
> |
possible that with longer simulation times, the (557) surface recovery |
| 812 |
> |
observed by Tao {\it et al}.\cite{Tao:2010} could also be recovered. |
| 813 |
|
|
| 814 |
|
%breaking of the double layer upon removal of CO |
| 815 |
|
\begin{figure}[H] |
| 816 |
|
\includegraphics[width=\linewidth]{EPS_doubleLayerBreaking} |
| 817 |
< |
\caption{Dynamics of an established (111) double step after removal of |
| 818 |
< |
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the removal |
| 819 |
< |
of CO. The presence of the CO helped maintain the stability of the |
| 820 |
< |
double step. Nearly immediately after the CO is removed, the step |
| 821 |
< |
edge reforms in a (100) configuration, which is also the step type |
| 768 |
< |
seen on clean (557) surfaces. The step separation involves |
| 817 |
> |
\caption{Behavior of an established (111) double step after removal of |
| 818 |
> |
the adsorbed CO: (A) 0~ps, (B) 100~ps, and (C) 1~ns after the |
| 819 |
> |
removal of CO. Nearly immediately after the CO is removed, the |
| 820 |
> |
step edge reforms in a (100) configuration, which is also the step |
| 821 |
> |
type seen on clean (557) surfaces. The step separation involves |
| 822 |
|
significant mixing of the lower and upper atoms at the edge.} |
| 823 |
|
\label{fig:breaking} |
| 824 |
|
\end{figure} |
| 889 |
|
Computing (CRC) at the University of Notre Dame. |
| 890 |
|
\end{acknowledgement} |
| 891 |
|
\newpage |
| 892 |
< |
\bibliography{firstTryBibliography} |
| 892 |
> |
\bibstyle{achemso} |
| 893 |
> |
\bibliography{COonPtAu} |
| 894 |
|
%\end{doublespace} |
| 895 |
|
|
| 896 |
|
\begin{tocentry} |
| 897 |
< |
|
| 898 |
< |
\includegraphics[height=2.8cm]{TOC_doubleLayer} |
| 899 |
< |
|
| 900 |
< |
A reconstructed Pt(557) surface after having been exposed to a dosage of CO equivalent to half a monolayer of coverage. |
| 901 |
< |
|
| 897 |
> |
\begin{wrapfigure}{l}{0.5\textwidth} |
| 898 |
> |
\begin{center} |
| 899 |
> |
\includegraphics[width=\linewidth]{TOC_doubleLayer} |
| 900 |
> |
\end{center} |
| 901 |
> |
\end{wrapfigure} |
| 902 |
> |
A reconstructed Pt(557) surface after 86~ns exposure to a half a |
| 903 |
> |
monolayer of CO. The double layer that forms is a result of |
| 904 |
> |
CO-mediated step-edge wandering as well as a burrowing mechanism that |
| 905 |
> |
helps lift edge atoms onto an upper terrace. |
| 906 |
|
\end{tocentry} |
| 907 |
|
|
| 908 |
|
\end{document} |
