| 8 |
|
higher binding energy the either a face centered cubic ({\sc fcc}) or |
| 9 |
|
hexagonal close-packed ({\sc hcp}) crystal structures.\cite{19521106} |
| 10 |
|
Icosahedra also have six five-fold symmetry axes that cannot be |
| 11 |
< |
extended indefinitely in three dimensions, which makes them long-range |
| 12 |
< |
translational order incommensurate with local icosahedral ordering. |
| 11 |
> |
extended indefinitely in three dimensions; long-range translational |
| 12 |
> |
order is therefore incommensurate with local icosahedral ordering. |
| 13 |
|
This does not preclude icosahedral clusters from possessing long-range |
| 14 |
|
{\it orientational} order. The ``frustrated'' packing of these |
| 15 |
|
icosahedral structures into dense clusters has been proposed as a |
| 128 |
|
values for {\it individual} icosahedral clusters, but these values are |
| 129 |
|
not invariant under rotations of the reference coordinate systems. |
| 130 |
|
Similar behavior is observed in the bond-orientational order |
| 131 |
< |
parameters for individual liquid-like structures. |
| 132 |
< |
|
| 133 |
< |
Additionally, both $Q_6$ and $\hat{W}_6$ are thought to have extreme |
| 134 |
< |
values for the icosahedral clusters.\cite{Steinhardt:1983mo} This |
| 135 |
< |
makes the $l=6$ bond-orientational order parameters particularly |
| 136 |
< |
useful in identifying the extent of local icosahedral ordering in |
| 137 |
< |
condensed phases. For example, a local structure which exhibits |
| 138 |
< |
$\hat{W}_6$ values near -0.17 is easily identified as an icosahedral |
| 139 |
< |
cluster and cannot be mistaken for distorted cubic or liquid-like |
| 140 |
< |
structures. |
| 131 |
> |
parameters for individual liquid-like structures. Additionally, both |
| 132 |
> |
$Q_6$ and $\hat{W}_6$ are thought to have extreme values for the |
| 133 |
> |
icosahedral clusters.\cite{Steinhardt:1983mo} This makes the $l=6$ |
| 134 |
> |
bond-orientational order parameters particularly useful in identifying |
| 135 |
> |
the extent of local icosahedral ordering in condensed phases. For |
| 136 |
> |
example, a local structure which exhibits $\hat{W}_6$ values near |
| 137 |
> |
-0.17 is easily identified as an icosahedral cluster and cannot be |
| 138 |
> |
mistaken for distorted cubic or liquid-like structures. |
| 139 |
|
|
| 140 |
|
One may use these bond orientational order parameters as an averaged |
| 141 |
|
property to obtain the extent of icosahedral ordering in a supercooled |
| 234 |
|
plot of $f_\textrm{icos}(T)$ as a function of temperature of the |
| 235 |
|
particles is given in figure \ref{fig:ficos}. As the particles cool, |
| 236 |
|
the fraction of local icosahedral ordering rises smoothly to a plateau |
| 237 |
< |
value. The larger particles (particularly the ones that were cooled |
| 238 |
< |
in a lower viscosity solvent) show a slightly smaller tendency towards |
| 237 |
> |
value. The smaller particles (particularly the ones that were cooled |
| 238 |
> |
in a higher viscosity solvent) show a slightly larger tendency towards |
| 239 |
|
icosahedral ordering. |
| 240 |
|
|
| 241 |
|
\begin{figure}[htbp] |
| 301 |
|
\label{fig:icoscluster} |
| 302 |
|
\end{figure} |
| 303 |
|
|
| 304 |
< |
Additionally, we have observed that those silver atoms that {\it do} |
| 305 |
< |
form local icosahedral structures are usually on the surface of the |
| 306 |
< |
nanoparticle, while the copper atoms which have local icosahedral |
| 307 |
< |
ordering are distributed more evenly throughout the nanoparticles. |
| 308 |
< |
Figure \ref{fig:Surface} shows this tendency as a function of distance |
| 309 |
< |
from the center of the nanoparticle. Silver, since it has a lower |
| 310 |
< |
surface free energy than copper, tends to coat the skins of the mixed |
| 311 |
< |
particles.\cite{Zhu:1997lr} This is true even for bimetallic particles |
| 312 |
< |
that have been prepared in the Ag (core) / Cu (shell) configuration. |
| 313 |
< |
Upon forming a liquid droplet, approximately 1 monolayer of Ag atoms |
| 314 |
< |
will rise to the surface of the particles. This can be seen visually |
| 315 |
< |
in figure \ref{fig:cross_sections} as well as in the density plots in |
| 316 |
< |
the bottom panel of figure \ref{fig:Surface}. This observation is |
| 319 |
< |
consistent with previous experimental and theoretical studies on |
| 320 |
< |
bimetallic alloys composed of noble |
| 304 |
> |
In contrast with the silver ordering behavior, the copper atoms which |
| 305 |
> |
have local icosahedral ordering are distributed more evenly throughout |
| 306 |
> |
the nanoparticles. Figure \ref{fig:Surface} shows this tendency as a |
| 307 |
> |
function of distance from the center of the nanoparticle. Silver, |
| 308 |
> |
since it has a lower surface free energy than copper, tends to coat |
| 309 |
> |
the skins of the mixed particles.\cite{Zhu:1997lr} This is true even |
| 310 |
> |
for bimetallic particles that have been prepared in the Ag (core) / Cu |
| 311 |
> |
(shell) configuration. Upon forming a liquid droplet, approximately 1 |
| 312 |
> |
monolayer of Ag atoms will rise to the surface of the particles. This |
| 313 |
> |
can be seen visually in figure \ref{fig:cross_sections} as well as in |
| 314 |
> |
the density plots in the bottom panel of figure \ref{fig:Surface}. |
| 315 |
> |
This observation is consistent with previous experimental and |
| 316 |
> |
theoretical studies on bimetallic alloys composed of noble |
| 317 |
|
metals.\cite{MainardiD.S._la0014306,HuangS.-P._jp0204206,Ramirez-Caballero:2006lr} |
| 318 |
|
Bond order parameters for surface atoms are averaged only over the |
| 319 |
|
neighboring atoms, so packing constraints that may prevent icosahedral |
