| 339 |
|
the surface.} |
| 340 |
|
\label{fig:Surface} |
| 341 |
|
\end{figure} |
| 342 |
< |
|
| 343 |
< |
The methods used by Sheng, He, and Ma to estimate the glass transition |
| 344 |
< |
temperature, $T_g$, in bulk Ag-Cu alloys involve finding |
| 345 |
< |
discontinuities in the slope of the average atomic volume, $\langle V |
| 346 |
< |
\rangle / N$, or enthalpy when plotted against the temperature of the |
| 347 |
< |
alloy. They obtained a bulk glass transition temperature, $T_g$ = 510 |
| 348 |
< |
K for a quenching rate of $2.5 \times 10^{13}$ K/s. |
| 342 |
> |
|
| 343 |
> |
Similar behavior has been observed by Luo {\it et al.} in their work |
| 344 |
> |
on amorphous Ni-Ag alloys. They used a common neighbor analysis (CNA) |
| 345 |
> |
technique that identified icosahedral ordering from simulated |
| 346 |
> |
structures that match experimental EXAFS spectra. Their simulated |
| 347 |
> |
structures exhibited icosahedral structures that were nearly always |
| 348 |
> |
centered on the smaller Ni atoms in the sample.\cite{luo:145502} |
| 349 |
> |
Details of the common neighbor analysis technique can be found in |
| 350 |
> |
Sheng {\it et al.}'s work on the glass transition in bulk Ag-Cu |
| 351 |
> |
alloys.\cite{sheng:184203} In the bulk Ag-Cu alloys, high quench |
| 352 |
> |
rates do lead to an increase in icosahedral ordering, although the |
| 353 |
> |
onset is much more gradual than what we have observed in the |
| 354 |
> |
bimetallic nanoparticles. |
| 355 |
|
|
| 356 |
< |
For simulations of nanoparticles, there is no periodic box, and |
| 357 |
< |
therefore, no easy way to compute the volume exactly. Instead, we |
| 358 |
< |
estimate the volume of our nanoparticles using Barber {\it et al.}'s |
| 359 |
< |
very fast quickhull algorithm to obtain the convex hull for the |
| 360 |
< |
collection of 3-d coordinates of all of atoms at each point in |
| 356 |
> |
Sheng {\it et al.} also estimated the glass transition temperature |
| 357 |
> |
($T_g$) in bulk Ag-Cu alloys involve by locating a discontinuity in |
| 358 |
> |
the slope of the average atomic volume, $\langle V \rangle / N$, or |
| 359 |
> |
enthalpy when plotted against the temperature of the alloy. They |
| 360 |
> |
obtained a bulk glass transition temperature, $T_g$ = 510 K for a |
| 361 |
> |
quenching rate of $2.5 \times 10^{13}$ K/s. For simulations of |
| 362 |
> |
nanoparticles, there is no periodic box, and therefore no facile way |
| 363 |
> |
of exactly computing the volume. Instead, we estimate the volume of |
| 364 |
> |
our nanoparticles using Barber {\it et al.}'s very fast quickhull |
| 365 |
> |
algorithm to obtain the convex hull for the collection of 3-d |
| 366 |
> |
coordinates of all of atoms at each point in |
| 367 |
|
time.~\cite{Barber96,qhull} The convex hull is the smallest convex |
| 368 |
|
polyhedron which includes all of the atoms, so the volume of this |
| 369 |
|
polyhedron is an excellent estimate of the volume of the nanoparticle. |
| 377 |
|
vs. temperature, we arrive at an estimate of $T_g$ that is |
| 378 |
|
approximately 488 K. We note that this temperature is somewhat below |
| 379 |
|
the onset of icosahedral ordering exhibited in the bond orientational |
| 380 |
< |
order parameters. It appears that icosahedral ordering sets in while |
| 381 |
< |
the system is still somewhat fluid, and is locked in place once the |
| 382 |
< |
temperature falls below $T_g$. We did not observe any dependence of |
| 383 |
< |
our estimates for $T_g$ on either the nanoparticle size or the value |
| 384 |
< |
of the interfacial conductance. However, the cooling rates and size |
| 385 |
< |
ranges we utilized are all sampled from a relatively narrow range, and |
| 386 |
< |
it is possible that much larger particles would have substantially |
| 387 |
< |
different values for $T_g$. Our estimates for the glass transition |
| 388 |
< |
temperatures for all three particle sizes and both interfacial |
| 389 |
< |
conductance values are shown in table \ref{table:Tg}. |
| 380 |
> |
order parameters. It appears that icosahedral ordering is initiated |
| 381 |
> |
while the system is still somewhat fluid, and is locked in place once |
| 382 |
> |
the temperature falls below $T_g$. We did not observe any dependence |
| 383 |
> |
of our estimates for $T_g$ on either the nanoparticle size or the |
| 384 |
> |
value of the interfacial conductance. However, the cooling rates and |
| 385 |
> |
size ranges we utilized are all sampled from a relatively narrow |
| 386 |
> |
range, and it is possible that much larger particles would have |
| 387 |
> |
substantially different values for $T_g$. Our estimates for the glass |
| 388 |
> |
transition temperatures for all three particle sizes and both |
| 389 |
> |
interfacial conductance values are shown in table \ref{table:Tg}. |
| 390 |
|
|
| 391 |
|
\begin{table} |
| 392 |
< |
\caption{Estimates of the glass transition temperatures $T_g$ for |
| 392 |
> |
\caption{Estimates of the glass transition temperatures ($T_g$) for |
| 393 |
|
three different sizes of bimetallic Ag$_6$Cu$_4$ nanoparticles cooled |
| 394 |
|
under two different values of the interfacial conductance, $G$.} |
| 395 |
|
\begin{center} |
| 397 |
|
\hline |
| 398 |
|
\hline |
| 399 |
|
Radius (\AA\ ) & Interfacial conductance & Effective cooling rate |
| 400 |
< |
(K/s $\times 10^{13}$) & & $T_g$ (K) \\ |
| 400 |
> |
($\times 10^{13}$ K/s) & $T_g$ (K) \\ |
| 401 |
|
20 & 87.5 & 2.4 & 477 \\ |
| 402 |
|
20 & 117 & 4.5 & 502 \\ |
| 403 |
|
30 & 87.5 & 1.3 & 491 \\ |
