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%!TEX root = /Users/charles/Desktop/nanoglass/nanoglass.tex |
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\section{Computational Methodology} |
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\label{sec:details} |
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Cu-core / Ag-shell and random alloy structures were constructed on an |
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underlying FCC lattice (4.09 {\AA}) at the bulk eutectic composition |
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$\mathrm{Ag}_6\mathrm{Cu}_4$. Three different sizes of nanoparticles |
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$\mathrm{Ag}_6\mathrm{Cu}_4$. All three compositions were considered although experimental results suggest that the random structure is the most likely composition after synthesis.\cite{Jiang:2005lr,gonzalo:5163} Three different sizes of nanoparticles |
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corresponding to a 20 \AA radius (1961 atoms), 30 {\AA} radius (6603 |
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atoms) and 40 {\AA} radius (15683 atoms) were constructed. These |
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initial structures were relaxed to their equilibrium structures at 20 |
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K for 20 ps and again at 300 K for 100 ps sampling from a |
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Maxwell-Boltzmann distribution at each temperature. |
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Maxwell-Boltzmann distribution at each temperature. |
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To mimic the effects of the heating due to laser irradiation, the |
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particles were allowed to melt by sampling velocities from the Maxwell |
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metallic atoms and the solvent, the effective viscosity is a |
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essentially a free parameter that must be tuned to give experimentally |
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relevant simulations. |
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\begin{figure}[htbp] |
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\centering |
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\includegraphics[width=\linewidth]{images/stochbound.pdf} |
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\caption{Methodology for nanoparticle cooling. Equations of motion for metal atoms contained in the outer 4 {\AA} were determined by Langevins' Equations of motion. Metal atoms outside this region were allowed to evolve under Newtonian dynamics.} |
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\label{fig:langevinSketch} |
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\end{figure} |
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The viscosity ($\eta$) can be tuned by comparing the cooling rate that |
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a set of nanoparticles experience with the known cooling rates for |
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those particles obtained via the laser heating experiments. |
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Values for the interfacial conductance have been determined by a |
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number of groups for similar nanoparticles and range from a low |
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$87.5\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ to $120\times 10^{6}$ |
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$(\mathrm{Wm^{-2}K^{-1}})$.\cite{XXX} |
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$(\mathrm{Wm^{-2}K^{-1}})$.\cite{hartlandPrv2007} Plech {\it et al.} reported a value for the interfacial conductance of $G=105\pm 15$ $(\mathrm{Wm^{-2}K^{-1}})$ and |
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$G=130\pm 15$ $(\mathrm{Wm^{-2}K^{-1}})$ for Pt nanoparticles.\cite{plech:195423,PhysRevB.66.224301} |
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We conducted our simulations at both ends of the range of |
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experimentally-determined values for the interfacial conductance. |
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$(\mathrm{Wm^{-2}K^{-1}})$ was used. Based on calculations we have |
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done using raw data from the Hartland group's thermal half-time |
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experiments on Au nanospheres, we believe that the true G values are |
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closer to the faster regime: $117\times 10^{6}$ |
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$(\mathrm{Wm^{-2}K^{-1}})$. |
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closer to the faster regime: $117\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$. |
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The rate of cooling for the nanoparticles in a molecular dynamics |
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simulation can then be tuned by changing the effective solvent |
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viscosity ($\eta$) until the nanoparticle cooling rate matches the |
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Fig. \ref{fig:images_cooling_plot}. It should be noted that the |
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Langevin thermostat produces cooling curves that are consistent with |
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Newtonian (single-exponential) cooling, which cannot match the cooling |
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profiles from Eq. \ref{eq:laplacetransform} exactly. |
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profiles from Eq. \ref{eq:laplacetransform} exactly. Fitting the Langevin cooling profiles to a single-exponential produces $\tau=25.576$ ps, $\tau=43.786$ ps, and $\tau=56.621$ ps for the 20, 30 and 40 {\AA} nanoparticles and a G of $87.5\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$. The faster cooling G of $117\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$ produced a $\tau=13.391$ ps, $\tau=30.426$ ps, $\tau=43.857$ ps for the 20, 30 and 40 {\AA} nanoparticles. |
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\begin{figure}[htbp] |
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\centering |
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$2\alpha_{ij}$ and include up to the sixth coordination shell in FCC |
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metals. |
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\subsection{Sampling single-temperature configurations from a cooling |
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trajectory} |
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%\subsection{Sampling single-temperature configurations from a cooling |
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%trajectory} |
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ffdsafjdksalfdsa |
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To better understand the structural changes occurring in the nanoparticles throughout the cooling trajectory, configurations were sampled at temperatures throughout the cooling trajectory. These configurations were then allowed to evolve under NVE dynamics to sample from the proper distribution in phase space. Figure \ref{fig:images_cooling_time_traces} illustrates this sampling. |
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\begin{figure}[htbp] |
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\centering |
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\includegraphics[height=3in]{images/cooling_time_traces.pdf} |
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\caption{Illustrative cooling profile for the 40 {\AA} nanoparticle evolving under stochastic boundary conditions corresponding to $G=$$87.5\times 10^{6}$ $(\mathrm{Wm^{-2}K^{-1}})$. At temperatures along the cooling trajectory, configurations were sampled and allowed to evolve in the NVE ensemble. These subsequent trajectories were analyzed for structural features associated with bulk glass formation.} |
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\label{fig:images_cooling_time_traces} |
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\end{figure} |
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