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. |