[ViewVC] Diff of: group/trunk/nanoglass/analysis.tex

Comparing trunk/nanoglass/analysis.tex (file contents):
Revision 3248 by chuckv, Thu Oct 4 22:07:13 2007 UTC vs.
Revision 3252 by gezelter, Mon Oct 8 21:36:02 2007 UTC

+\label{fig:q6}
+\end{figure}
-+
+The probability distributions of local order can be used to generate
-+
+free energy surfaces using the local orientational ordering as a
-+
+reaction coordinate.  By making the simple statistical equivalence
-+
+between the free energy and the probabilities of occupying certain
-+
+states,
-+
+\begin{equation}
-+
+g(\hat{W}_6) = - k_B T \ln p(\hat{W}_6),
-+
+\end{equation}
-+
+we can obtain a sequence of free energy surfaces (as a function of
-+
+temperature) for the local ordering around central atoms within our
-+
+particles.  Free energy surfaces for the 40 \AA\ particle at a range
-+
+of temperatures are shown in figure \ref{fig:freeEnergy}.  Note that
-+
+at all temperatures, the liquid-like structures are global minima on
-+
+the free energy surface, while the local icosahedra appear as local
-+
+minima once the temperature has fallen below 528 K.  As the
-+
+temperature falls, it is possible for substructures to become trapped
-+
+in the local icosahedral well, and if the cooling is rapid enough,
-+
+this trapping leads to vitrification.  A similar analysis of the free
-+
+energy surface for orientational order in bulk glass formers can be
-+
+found in the work of van~Duijneveldt and
-+
+Frenkel.\cite{duijneveldt:4655}
-+
-+
+\begin{figure}[htbp]
-+
+\centering
-+
+\includegraphics[width=5in]{images/freeEnergyVsW6.pdf}
-+
+\caption{Free energy as a function of the orientational order
-+
+parameter ($\hat{W}_6$) for 40 \AA bimetallic nanoparticles as they
-+
+are cooled from 902 K to 310 K.  As the particles cool below 528 K, a
-+
+local minimum in the free energy surface appears near the perfect
-+
+icosahedral ordering ($\hat{W}_6 = -0.17$).  At all temperatures,
-+
+liquid-like structures are a global minimum on the free energy
-+
+surface, but if the cooling rate is fast enough, substructures
-+
+may become trapped with local icosahedral order, leading to the
-+
+formation of a glass.}
-+
+\label{fig:freeEnergy}
-+
+\end{figure}
-+
+We have also calculated the fraction of atomic centers which have
+strong local icosahedral order:
+\begin{equation}
+\AA\ nanoparticle.  Local icosahedral ordering around copper atoms is
+much more prevalent than around silver atoms.}
+\label{fig:AgVsCu}
-+
+\end{figure}
-+
-+
+The locations of these icosahedral centers are not uniformly
-+
+distrubted throughout the particles.  In figure \ref{fig:icoscluster}
-+
+we show snapshots of the centers of the local icosahedra (i.e. any
-+
+atom which exhibits a local bond orientational order parameter
-+
+$\hat{W}_6 < -0.15$).  At high temperatures, the icosahedral centers
-+
+are transitory, existing only for a few fs before being reabsorbed
-+
+into the liquid droplet.  As the particle cools, these centers become
-+
+fixed at certain locations, and additional icosahedra develop
-+
+throughout the particle, clustering around the sites where the
-+
+structures originated.  There is a strong preference for icosahedral
-+
+ordering near the surface of the particles.  Identification of these
-+
+structures by the type of atom shows that the silver-centered
-+
+icosahedra are evident only at the surface of the particles.
-+
-+
+\begin{figure}[htbp]
-+
+\centering
-+
+\begin{tabular}{c c c}
-+
+\includegraphics[width=2.1in]{images/Cu_Ag_random_30A_liq_icosonly.pdf}
-+
+\includegraphics[width=2.1in]{images/Cu_Ag_random_30A__0007_icosonly.pdf}
-+
+\includegraphics[width=2.1in]{images/Cu_Ag_random_30A_glass_icosonly.pdf}
-+
+\end{tabular}
-+
+\caption{Centers of local icosahedral order ($\hat{W}_6<0.15$) at 900
-+
+K, 471 K and 315 K for the 30 \AA\ nanoparticle cooled with an
-+
+interfacial conductance $G = 87.5 \times 10^{6}$
-+
+$\mathrm{Wm^{-2}K^{-1}}$. Silver atoms (blue) exhibit icosahedral
-+
+order at the surface of the nanoparticle while copper icosahedral
-+
+centers (green) are distributed throughout the nanoparticle.  The
-+
+icosahedral centers appear to cluster together and these clusters
-+
+increase in size with decreasing temperature.}
-+
+\label{fig:icoscluster}
+\end{figure}
+Additionally, we have observed that those silver atoms that {\it do}
+silver and copper to form local icosahedral structures in a bulk glass
+differs from our observations on nanoparticles.
-–
+\begin{figure}[htbp]
+\centering
-–
+\begin{tabular}{c c c}
-–
+\includegraphics[width=2.1in]{images/Cu_Ag_random_30A_liq_icosonly.pdf}
-–
+\includegraphics[width=2.1in]{images/Cu_Ag_random_30A__0007_icosonly.pdf}
-–
+\includegraphics[width=2.1in]{images/Cu_Ag_random_30A_glass_icosonly.pdf}
-–
+\end{tabular}
-–
+\caption{Appearance of icosahedral clusters ($\hat{W}_6<0.15$) at 900 K, 471 K and 315 K for the 30 \AA\ nanoparticle cooled at the slower cooling rate. Silver atoms (blue) mostly exhibit icosahedral order at the surface whereas clusters of Copper atoms (green) with icosahedral order are distributed throughout the nanoparticle and increase in size with decreasing temperature.}
-–
+\label{fig:icoscluster}
-–
+\end{figure}
-–
-–
-–
+\begin{figure}[htbp]
-–
+\centering
+\includegraphics[width=5in]{images/dens_fracr_stacked_plot.pdf}
+\caption{Appearance of icosahedral clusters around central silver atoms
+is largely due to the presence of these silver atoms at or near the

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Comparing trunk/nanoglass/analysis.tex (file contents): Revision 3248 by chuckv, Thu Oct 4 22:07:13 2007 UTC vs. Revision 3252 by gezelter, Mon Oct 8 21:36:02 2007 UTC

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Comparing trunk/nanoglass/analysis.tex (file contents):
Revision 3248 by chuckv, Thu Oct 4 22:07:13 2007 UTC vs.
Revision 3252 by gezelter, Mon Oct 8 21:36:02 2007 UTC