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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.) One of the side effects of |
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absorption of laser radiation at these frequencies is the rapid |
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(sub-picosecond) heating of the electronic degrees of freedom in the |
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metal. This hot electron gas quickly transfers heat to the phonon |
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modes of the lattice, resulting in a rapid heating of the metal |
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particles. |
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Since metallic nanoparticles have a large surface area to volume |
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ratio, many of the metal atoms are at surface locations and experience |
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relatively weak bonding. This is observable in a lowering of the |
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melting temperatures and a substantial softening of the bulk modulus |
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of these particles when compared with bulk metallic samples. One of |
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the side effects of the excitation of small metallic nanoparticles at |
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the plasmon resonance is the facile creation of liquid metal |
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droplets. |
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Much of the experimental work on this subject has been carried out in |
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the Hartland and von~Plessen groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003lr,Petrova:2007qy,Link:2000lr} These experiments mostly use the technique of time-resolved optical pump-probe spectroscopy where a pump laser pulse serves to excite conduction band electrons in the nanoparticle and a following probe laser pulse allows the electron-phonon coupling to be observed as a function of time. Hu and Hartland have observed a direct relation between the size of the nanoparticle and the observed cooling rate using such pump-probe techniques.\cite{HuM._jp020581+} Pleach {\it et al.} have use pulsed x-ray scattering as a probe to directly access changes to atomic structure following pump excitation.\cite{plech:195423} They further determined that heat transfer in nanoparticles to the surrounding solvent is goverened by interfacial dynamics and not the thermal transport properties of the solvent. |
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Since these experiments are often 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 also a relatively rapid process. |
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In our recent simulation study of the laser excitation of gold |
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nanoparticles,\cite{VardemanC.F._jp051575r} we observed that the cooling rate for these |
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particles (10$^{11}$-10$^{12}$ K/s) is in excess of the cooling rate |
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required for glass formation in bulk metallic alloys. Given this |
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fact, it may be possible to use laser excitation to melt, alloy and |
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quench metallic nanoparticles in order to form metallic glass |
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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 a |
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well-known exception to this rule and are only miscible in the liquid |
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state given equilibrium conditions. Below the eutectic temperature of |
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779 $^\circ$C and composition (60.1\% Ag, 39.9\% Cu), the |
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solid alloys of Ag and Cu will phase separate into Ag and Cu rich |
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$\alpha$ and $\beta$ phases, respectively. 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, $\Delta H$ is on the order |
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of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid solutions may be |
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formed by undercooling, and under these conditions, a |
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compositionally-disordered $\gamma$ fcc phase can be formed. |
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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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$\Delta H$, supersaturated crystalline solutions are typically |
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obtained rather than an amorphous phase. Higher $\Delta H$ systems, |
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such as Ag-Ni, are immiscible even in liquid states, but they tend to |
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form metastable alloys much more readily than Ag-Cu. If present, the |
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amorphous Ag-Cu phase is usually seen as the minority phase in most |
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experiments. Because of this unique crystalline-amorphous behavior, |
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the Ag-Cu system has been widely studied. Methods for creating such |
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bulk phase structures include splat quenching, vapor deposition, ion |
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beam mixing and mechanical alloying. Both structural |
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\cite{sheng:184203} and dynamic\cite{Vardeman-II:2001jn} |
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computational studies have also been 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 the pure metals. For |
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bimetallic nanoparticles with 40\% Ag an absorption peak is seen |
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between 400-550 nm. With increasing Ag content, the SPR shifts |
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towards the blue, with the peaks nearly coincident at a composition of |
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57\% Ag. Gonzalo {\it et al.} cited the existence of a single broad |
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resonance peak as evidence of a mixed alloy particle rather than a |
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phase segregated system. Unfortunately, they were unable to determine |
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whether the mixed nanoparticles were an amorphous phase or a |
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supersaturated crystalline phase. One consequence of embedding the |
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Ag-Cu nanoparticles in a glass matrix is that the SPR can be shifted |
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because of the nanoparticle-glass matrix |
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interaction.\cite{De:1996ta,Roy:2003dy} |
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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 nanoparticles |
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differs significantly from the bulk in that atoms are confined to a |
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roughly spherical volume and cannot explore any region larger than the |
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particle radius ($R$). In these confined geometries, $\langle r^2(t) |
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\rangle$ approaches a limiting value of $3R^2/40$.\cite{ShibataT._ja026764r} This limits the |
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utility of dynamical measures of glass formation when studying |
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nanoparticles. |
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However, glassy materials exhibit strong icosahedral ordering among |
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nearest-neghbors in contrast to crystalline or liquid structures. |
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Local icosahedral structures are the three-dimensional equivalent of |
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covering a two-dimensional plane with 5-sided tiles; they cannot be |
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used to tile space in a periodic fashion, and are therefore an |
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indicator of non-periodic packing in amorphous solids. Steinhart {\it |
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et al.} defined an orientational bond order parameter that is |
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sensitive to icosahedral ordering.\cite{Steinhardt:1983mo} This bond |
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order parameter can therefore be used to characterize glass formation |
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in liquid and solid 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 a amorphous |
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structure.\cite{Strandburg:1992qy} The nearest neighbor information was |
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obtained from pair correlation functions, common neighbor analysis and |
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bond order parameters.\cite{Steinhardt:1983mo} It should be noted that |
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these studies used single component systems with cooling rates that |
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are only obtainable in computer simulations and particle sizes less |
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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. Icosahedral structures have |
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also been reported in nanoparticles, particularly multiply twinned |
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particles.\cite{Ascencio:2000qy} |
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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 to volume ratio aid Ag-Cu |
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nanoparticles in rapid cooling and formation of an amorphous state? |
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Would a predisposition to isosahedral ordering in nanoparticles also |
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allow for easier formation of an amorphous state and what is the |
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preferred ordering in a amorphous nanoparticle? Nanoparticles have |
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been shown to have size dependent melting |
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transition,\cite{Buffat:1976yq} and we would expect a similar trend |
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to follow for the glass transition temperature. |
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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 in silico to mimic |
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real experimental conditions. The simulation parameters have been |
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tuned to the degree possible to match experimental conditions, and we |
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discusss both the icosahedral ordering in the system, as well as the |
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clustering of icosahedral centers that we observed. |
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