| 161 |
|
Coulomb potential. For this work, we have used classical molecular |
| 162 |
|
dynamics with potential energy surfaces that are specifically tuned |
| 163 |
|
for transition metals. In particular, we used the EAM potential for |
| 164 |
< |
Au-Au and Pt-Pt interactions\cite{EAM}. The CO was modeled using a rigid |
| 164 |
> |
Au-Au and Pt-Pt interactions.\cite{EAM} The CO was modeled using a rigid |
| 165 |
|
three-site model developed by Straub and Karplus for studying |
| 166 |
|
photodissociation of CO from myoglobin.\cite{Straub} The Au-CO and |
| 167 |
|
Pt-CO cross interactions were parameterized as part of this work. |
| 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 |
| 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 |
| 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 |
| 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 |
| 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. |
| 550 |
> |
stability strongly and many atoms that had been tracked for mobility |
| 551 |
> |
data have now been buried. By performing the same diffusion |
| 552 |
> |
calculation but on a shorter run time (20~ns), only including data |
| 553 |
> |
before the formation of the first double layer, we obtain the larger |
| 554 |
> |
values for both $\mathbf{D}_{\parallel}$ and $\mathbf{D}_{\perp}$ |
| 555 |
> |
at the 50\% coverage as seen in Figure \ref{fig:diff}. |
| 556 |
|
This places the parallel diffusion constant more closely in line with the |
| 557 |
|
expected trend, while the perpendicular diffusion constant does not |
| 558 |
|
drop as far. A secondary explanation arising from our analysis of the |
| 560 |
|
surface has with respect to overcoming surface diffusion of Pt. If the |
| 561 |
|
coverage is too sparse, the Pt engages in minimal interactions and |
| 562 |
|
thus minimal diffusion. As coverage increases, there are more favorable |
| 563 |
< |
arrangements of CO on the surface allowing the formation of a path, |
| 563 |
> |
arrangements of CO on the surface allowing for the formation of a path, |
| 564 |
|
a minimum energy trajectory, for the adatom to explore the surface. |
| 565 |
|
As the CO is constantly moving on the surface, this path is constantly |
| 566 |
|
changing. If the coverage becomes too great, the paths could |
| 570 |
|
|
| 571 |
|
|
| 572 |
|
\subsubsection{Dynamics of double layer formation} |
| 573 |
< |
The increased diffusion on Pt at the higher |
| 574 |
< |
CO coverages plays a primary role in double layer formation. However, this is not |
| 575 |
< |
a complete explanation -- the 33\%~Pt system |
| 576 |
< |
has higher diffusion constants but did not show |
| 577 |
< |
any signs of edge doubling in the observed run time. On the |
| 578 |
< |
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 |
| 579 |
< |
110~ns (150~ns total). Previous experimental |
| 580 |
< |
work gives insight into the upper bounds of the |
| 581 |
< |
time required for step coalescence.\cite{Williams:1991,Pearl} |
| 573 |
> |
The increased diffusion on Pt at the higher CO coverages |
| 574 |
> |
plays a primary role in double layer formation. However, |
| 575 |
> |
this is not a complete explanation -- the 33\%~Pt system |
| 576 |
> |
has higher diffusion constants but did not show any signs |
| 577 |
> |
of edge doubling in the observed run time. On the |
| 578 |
> |
50\%~Pt system, one layer formed within the first 40~ns |
| 579 |
> |
of simulation time, while two more were formed as the |
| 580 |
> |
system was allowed to run for an additional |
| 581 |
> |
110~ns (150~ns total). This suggests that this reconstruction is |
| 582 |
> |
a rapid process and that the previously mentioned upper bound |
| 583 |
> |
will be lowered as experimental techniques continue to improve.\cite{Williams:1991,Pearl} |
| 584 |
|
In this system, as seen in Figure \ref{fig:reconstruct}, the first |
| 585 |
|
appearance of a double layer, appears at 19~ns |
| 586 |
|
into the simulation. Within 12~ns of this nucleation event, nearly half of the step has |
| 590 |
|
appearance of the first nucleation event to the first observed double layer, the process took $\sim$20~ns. Another |
| 591 |
|
$\sim$40~ns was necessary for the layer to completely straighten. |
| 592 |
|
The other two layers in this simulation formed over periods of |
| 593 |
< |
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 |
> |
22~ns and 42~ns respectively. A possible explanation |
| 594 |
|
for this rapid reconstruction is the elevated temperatures |
| 595 |
|
under which our systems were simulated. It is probable that the process would |
| 596 |
< |
take longer at lower temperatures. |
| 596 |
> |
take longer at lower temperatures. Additionally, our measured times for completion |
| 597 |
> |
of the doubling after the appearance of a nucleation site are likely affected by our |
| 598 |
> |
constrained axes. A longer step-edge will likely take longer to ``zipper''. However, |
| 599 |
> |
the first appearance of a nucleation site will likely occur more quickly due to its stochastic nature. |
| 600 |
|
|
| 601 |
|
|
| 602 |
|
|
| 700 |
|
Pt atoms. To test this hypothesis, numerous configurations of |
| 701 |
|
CO in varying quantities were arranged on the higher and lower plateaus |
| 702 |
|
around a step on a otherwise clean Pt(557) surface. A few sample |
| 703 |
< |
configurations are displayed in Figure \ref{fig:lambdaTable}, with |
| 703 |
> |
configurations are displayed in Figure \ref{fig:SketchGraphic}, with |
| 704 |
|
energies at various positions along the path displayed in Table |
| 705 |
< |
\ref{tab:rxcoord}. Certain configurations of CO, cases B and D for |
| 705 |
> |
NO TABLE. Certain configurations of CO, cases B and D for |
| 706 |
|
example, can have quite strong energetic reasons for breaking |
| 707 |
|
away from the step-edge. Although the packing of these configurations |
| 708 |
|
is unlikely until CO coverage has reached a high enough value. |
