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\section{Introduction} |
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%!TEX root = /Users/charles/Desktop/nanoglass/nanoglass.tex |
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\section{Introduction} |
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Excitation of the plasmon resonance in metallic nanoparticles has |
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attracted enormous interest in the past several years. This is partly |
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due to the location of the plasmon band in the near IR for particles |
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in a wide range of sizes and geometries. Living tissue is nearly |
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transparent in the near IR, and for this reason, there is an |
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unrealized potential for metallic nanoparticles to be used in both |
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diagnostic and therapeutic settings.\cite{West:2003fk,Hu:2006lr} One |
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of the side effects of absorption of laser radiation at these |
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frequencies is the rapid (sub-picosecond) heating of the electronic |
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degrees of freedom in the metal. This hot electron gas quickly |
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transfers heat to the phonon modes of the particle, resulting in a |
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rapid heating of the lattice of the metal particles. Since metallic |
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nanoparticles have a large surface area to volume ratio, many of the |
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metal atoms are at surface locations and experience relatively weak |
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bonding. This is observable in a lowering of the melting temperatures |
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of these particles when compared with bulk metallic |
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samples.\cite{Buffat:1976yq,Dick:2002qy} One of the side effects of |
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the excitation of small metallic nanoparticles at the plasmon |
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resonance is the facile creation of liquid metal |
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droplets.\cite{Mafune01,HartlandG.V._jp0276092,Link:2000lr,Plech:2003yq,plech:195423,Plech:2007rt} |
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Much of the experimental work on this subject has been carried out in |
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the Hartland, El-Sayed and Plech |
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groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003lr,Petrova:2007qy,Link:2000lr,plech:195423,Plech:2007rt} |
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These experiments mostly use the technique of time-resolved optical |
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pump-probe spectroscopy, where a pump laser pulse serves to excite |
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conduction band electrons in the nanoparticle and a following probe |
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laser pulse allows observation of the time evolution of the |
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electron-phonon coupling. Hu and Hartland have observed a direct |
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relation between the size of the nanoparticle and the observed cooling |
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rate using such pump-probe techniques.\cite{Hu:2004lr} Plech {\it et |
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al.} have use pulsed x-ray scattering as a probe to directly access |
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changes to atomic structure following pump |
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excitation.\cite{plech:195423} They further determined that heat |
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transfer in nanoparticles to the surrounding solvent is goverened by |
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interfacial dynamics and not the thermal transport properties of the |
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solvent. This is in agreement with Cahill,\cite{Wilson:2002uq} |
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but opposite to the conclusions in Reference \citen{Hu:2004lr}. |
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Since these experiments are carried out in condensed phase |
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surroundings, the large surface area to volume ratio makes the heat |
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transfer to the surrounding solvent a relatively rapid process. In our |
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recent simulation study of the laser excitation of gold |
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nanoparticles,\cite{VardemanC.F._jp051575r} we observed that the |
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cooling rate for these particles (10$^{11}$-10$^{12}$ K/s) is in |
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excess of the cooling rate required for glass formation in bulk |
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metallic alloys.\cite{Greer:1995qy} Given this fact, it may be |
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possible to use laser excitation to melt, alloy and quench metallic |
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nanoparticles in order to form glassy nanobeads. |
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To study whether or not glass nanobead formation is feasible, we have |
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chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a |
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model system because it is an experimentally known glass former, and |
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has been used previously as a theoretical model for glassy |
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dynamics.\cite{Vardeman-II:2001jn} The Hume-Rothery rules suggest that |
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alloys composed of Copper and Silver should be miscible in the solid |
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state, because their lattice constants are within 15\% of each |
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another.\cite{Kittel:1996fk} Experimentally, however Ag-Cu alloys are |
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a well-known exception to this rule and are only miscible in the |
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liquid state given equilibrium conditions.\cite{Massalski:1986rt} |
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Below the eutectic temperature of 779 $^\circ$C and composition |
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(60.1\% Ag, 39.9\% Cu), the solid alloys of Ag and Cu will phase |
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separate into Ag and Cu rich $\alpha$ and $\beta$ phases, |
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respectively.\cite{Banhart:1992sv,Ma:2005fk} This behavior is due to a |
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positive heat of mixing in both the solid and liquid phases. For the |
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one-to-one composition fcc solid solution, $\Delta H_{\rm mix}$ is on |
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the order of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid |
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solutions may be formed by undercooling, and under these conditions, a |
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compositionally-disordered $\gamma$ fcc phase can be |
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formed.\cite{najafabadi:3144} |
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Metastable alloys composed of Ag-Cu were first reported by Duwez in |
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1960 and were created by using a ``splat quenching'' technique in |
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which a liquid droplet is propelled by a shock wave against a cooled |
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metallic target.\cite{duwez:1136} Because of the small positive |
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$\Delta H_{\rm mix}$, supersaturated crystalline solutions are |
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typically obtained rather than an amorphous phase. Higher $\Delta |
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H_{\rm mix}$ systems, such as Ag-Ni, are immiscible even in liquid |
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states, but they tend to form metastable alloys much more readily than |
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Ag-Cu. If present, the amorphous Ag-Cu phase is usually seen as the |
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minority phase in most experiments. Because of this unique |
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crystalline-amorphous behavior, the Ag-Cu system has been widely |
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studied. Methods for creating such bulk phase structures include splat |
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quenching, vapor deposition, ion beam mixing and mechanical |
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alloying. Both structural \cite{sheng:184203} and |
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dynamic\cite{Vardeman-II:2001jn} computational studies have also been |
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performed on this system. |
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Although bulk Ag-Cu alloys have been studied widely, this alloy has |
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been mostly overlooked in nanoscale materials. The literature on |
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alloyed metallic nanoparticles has dealt with the Ag-Au system, which |
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has the useful property of being miscible on both solid and liquid |
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phases. Nanoparticles of another miscible system, Au-Cu, have been |
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successfully constructed using techniques such as laser |
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ablation,\cite{Malyavantham:2004cu} and the synthetic reduction of |
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metal ions in solution.\cite{Kim:2003lv} Laser induced alloying has |
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been used as a technique for creating Au-Ag alloy particles from |
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core-shell particles.\cite{Hartland:2003lr} To date, attempts at |
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creating Ag-Cu nanoparticles have used ion implantation to embed |
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nanoparticles in a glass matrix.\cite{De:1996ta,Magruder:1994rg} These |
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attempts have been largely unsuccessful in producing mixed alloy |
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nanoparticles, and instead produce phase segregated or core-shell |
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structures. |
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One of the more successful attempts at creating intermixed Ag-Cu |
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nanoparticles used alternate pulsed laser ablation and deposition in |
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an amorphous Al$_2$O$_3$ matrix.\cite{gonzalo:5163} Surface plasmon |
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resonance (SPR) of bimetallic core-shell structures typically show two |
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distinct resonance peaks where mixed particles show a single shifted |
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and broadened resonance.\cite{Hodak:2000rb} The SPR for pure silver |
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occurs at 400 nm and for copper at 570 nm.\cite{HengleinA._jp992950g} |
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On Al$_2$O$_3$ films, these resonances move to 424 nm and 572 nm for |
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the pure metals. For bimetallic nanoparticles with 40\% Ag an |
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absorption peak is seen between 400-550 nm. With increasing Ag |
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content, the SPR shifts towards the blue, with the peaks nearly |
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coincident at a composition of 57\% Ag. Gonzalo {\it et al.} cited the |
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existence of a single broad resonance peak as evidence of an alloyed |
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particle rather than a phase segregated system. However, spectroscopy |
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may not be able to tell the difference between alloyed particles and |
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mixtures of segregated particles. High-resolution electron microscopy |
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has so far been unable to determine whether the mixed nanoparticles |
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were an amorphous phase or a supersaturated crystalline phase. |
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Characterization of glassy behavior by molecular dynamics simulations |
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is typically done using dynamic measurements such as the mean squared |
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displacement, $\langle r^2(t) \rangle$. Liquids exhibit a mean squared |
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displacement that is linear in time (at long times). Glassy materials |
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deviate significantly from this linear behavior at intermediate times, |
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entering a sub-linear regime with a return to linear behavior in the |
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infinite time limit.\cite{Kob:1999fk} However, diffusion in |
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nanoparticles differs significantly from the bulk in that atoms are |
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confined to a roughly spherical volume and cannot explore any region |
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larger than the particle radius ($R$). In these confined geometries, |
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$\langle r^2(t) \rangle$ approaches a limiting value of |
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$3R^2/40$.\cite{ShibataT._ja026764r} This limits the utility of |
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dynamical measures of glass formation when studying nanoparticles. |
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However, glassy materials exhibit strong icosahedral ordering among |
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nearest-neghbors (in contrast with crystalline and liquid-like |
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configurations). Local icosahedral structures are the |
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three-dimensional equivalent of covering a two-dimensional plane with |
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5-sided tiles; they cannot be used to tile space in a periodic |
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fashion, and are therefore an indicator of non-periodic packing in |
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amorphous solids. Steinhart {\it et al.} defined an orientational bond |
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order parameter that is sensitive to icosahedral |
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ordering.\cite{Steinhardt:1983mo} This bond order parameter can |
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therefore be used to characterize glass formation in liquid and solid |
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solutions.\cite{wolde:9932} |
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Theoretical molecular dynamics studies have been performed on the |
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formation of amorphous single component nanoclusters of either |
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gold,\cite{Chen:2004ec,Cleveland:1997jb,Cleveland:1997gu} or |
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nickel,\cite{Gafner:2004bg,Qi:2001nn} by rapid cooling($\thicksim |
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10^{12}-10^{13}$ K/s) from a liquid state. All of these studies found |
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icosahedral ordering in the resulting structures produced by this |
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rapid cooling which can be evidence of the formation of an amorphous |
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structure.\cite{Strandburg:1992qy} The nearest neighbor information |
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was obtained from pair correlation functions, common neighbor analysis |
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and bond order parameters.\cite{Steinhardt:1983mo} It should be noted |
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that these studies used single component systems with cooling rates |
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that are only obtainable in computer simulations and particle sizes |
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less than 20\AA. Single component systems are known to form amorphous |
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states in small clusters,\cite{Breaux:rz} but do not generally form |
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amorphous structures in bulk materials. |
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Since the nanoscale Ag-Cu alloy has been largely unexplored, many |
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interesting questions remain about the formation and properties of |
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such a system. Does the large surface area to volume ratio aid Ag-Cu |
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nanoparticles in rapid cooling and formation of an amorphous state? |
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Nanoparticles have been shown to have a size dependent melting |
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transition ($T_m$),\cite{Buffat:1976yq,Dick:2002qy} so we might expect |
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a similar trend to follow for the glass transition temperature |
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($T_g$). By analogy, bulk metallic glasses exhibit a correlation |
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between $T_m$ and $T_g$ although such dependence is difficult to |
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establish because of the dependence of $T_g$ on cooling rate and the |
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process by which the glass is formed.\cite{Wang:2003fk} It has also |
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been demonstrated that there is a finite size effect depressing $T_g$ |
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in polymer glasses in confined geometries.\cite{Alcoutlabi:2005kx} |
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In the sections below, we describe our modeling of the laser |
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excitation and subsequent cooling of the particles {\it in silico} to |
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mimic real experimental conditions. The simulation parameters have |
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been tuned to the degree possible to match experimental conditions, |
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and we discusss both the icosahedral ordering in the system, as well |
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as the clustering of icosahedral centers that we observed. |
