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\section{Introduction} |
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Excitation of the plasmon resonance in metallic nanoparticles has attracted enormous interest in the past several years. This is partly due to the location of the plasmon band in the near IR for particles in a wide range of sizes and geometries. (Living tissue is nearly transparent in the near IR, and for this reason, there is an unrealized potential for metallic nanoparticles to be used in both diagnostic and therapeutic settings.\cite{West:2003fk,Hu:2006lr} One of the side effects of absorption of laser radiation at these frequencies is the rapid (sub-picosecond) heating of the electronic degrees of freedom in the metal. This hot electron gas quickly transfers heat to the phonon modes of the lattice, resulting in a rapid heating of the metal particles. |
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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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|
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Since metallic nanoparticles have a large surface area to volume ratio, many of the metal atoms are at surface locations and experience relatively weak bonding. This is observable in a lowering of the melting temperatures and of these particles when compared with bulk metallic samples.\cite{Buffat:1976yq,Dick:2002qy} One of the side effects of the excitation of small metallic nanoparticles at the plasmon resonance is the facile creation of liquid metal droplets. |
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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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|
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< |
Much of the experimental work on this subject has been carried out in 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 observation of the time evolution of the electron-phonon coupling. 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{Hu:2004lr} Plech {\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.\cite{Mafune01,HartlandG.V._jp0276092,Link:2000lr,Plech:2003yq,plech:195423,Plech:2007rt} |
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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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|
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< |
Since these experiments are often carried out in condensed phase surroundings, the large surface area to volume ratio makes the heat transfer to the surrounding solvent also a relatively rapid process. In our recent simulation study of the laser excitation of gold nanoparticles,\cite{VardemanC.F._jp051575r} we observed that the cooling rate for these particles (10$^{11}$-10$^{12}$ K/s) is in excess of the cooling rate required for glass formation in bulk metallic alloys. Given this fact, it may be possible to use laser excitation to melt, alloy and quench metallic 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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|
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< |
To study whether or not glass nanobead formation is feasible, we have chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a model system because it is an experimentally known glass former and has been used previously as a theoretical model for glassy dynamics.\cite{Vardeman-II:2001jn} The Hume-Rothery rules suggest that alloys composed of Copper and Silver should be miscible in the solid state, because their lattice constants are within 15\% of each another.\cite{Kittel:1996fk} Experimentally, however Ag-Cu alloys are a well-known exception to this rule and are only miscible in the liquid state given equilibrium conditions.\cite{Massalski:1986rt} Below the eutectic temperature of 779 $^\circ$C and composition (60.1\% Ag, 39.9\% Cu), the solid alloys of Ag and Cu will phase separate into Ag and Cu rich $\alpha$ and $\beta$ phases, respectively.\cite{Banhart:1992sv,Ma:2005fk} This behavior is due to a positive heat of mixing in both the solid and liquid phases. For the one-to-one composition fcc solid solution, $\Delta H_{\rm mix}$ is on the order of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid solutions may be formed by undercooling, and under these conditions, a compositionally-disordered $\gamma$ fcc phase can be 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 |
| 80 |
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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 |
| 83 |
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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 |
| 85 |
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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 |
| 88 |
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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 |
| 90 |
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quenching, vapor deposition, ion beam mixing and mechanical |
| 91 |
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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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|
| 95 |
< |
Metastable alloys composed of Ag-Cu were first reported by Duwez in 1960 and were created by using a ``splat quenching'' technique in which a liquid droplet is propelled by a shock wave against a cooled metallic target.\cite{duwez:1136} Because of the small positive $\Delta H_{\rm mix}$, supersaturated crystalline solutions are typically obtained rather than an amorphous phase. Higher $\Delta H_{\rm mix}$ systems, such as Ag-Ni, are immiscible even in liquid states, but they tend to form metastable alloys much more readily than Ag-Cu. If present, the amorphous Ag-Cu phase is usually seen as the minority phase in most experiments. Because of this unique crystalline-amorphous behavior, the Ag-Cu system has been widely studied. Methods for creating such bulk phase structures include splat quenching, vapor deposition, ion beam mixing and mechanical alloying. Both structural \cite{sheng:184203} and dynamic\cite{Vardeman-II:2001jn} 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 |
| 107 |
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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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|
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< |
Although bulk Ag-Cu alloys have been studied widely, this alloy has been mostly overlooked in nanoscale materials. The literature on alloyed metallic nanoparticles has dealt with the Ag-Au system, which has the useful property of being miscible on both solid and liquid phases. Nanoparticles of another miscible system, Au-Cu, have been successfully constructed using techniques such as laser ablation,\cite{Malyavantham:2004cu} and the synthetic reduction of metal ions in solution.\cite{Kim:2003lv} Laser induced alloying has been used as a technique for creating Au-Ag alloy particles from core-shell particles.\cite{Hartland:2003lr} To date, attempts at creating Ag-Cu nanoparticles have used ion implantation to embed nanoparticles in a glass matrix.\cite{De:1996ta,Magruder:1994rg} These attempts have been largely unsuccessful in producing mixed alloy nanoparticles, and instead produce phase segregated or core-shell 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 |
| 114 |
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resonance (SPR) of bimetallic core-shell structures typically show two |
| 115 |
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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 |
| 117 |
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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 |
| 120 |
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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 |
| 125 |
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may not be able to tell the difference between alloyed particles and |
| 126 |
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mixtures of segregated particles. High-resolution electron microscopy |
| 127 |
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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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|
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< |
One of the more successful attempts at creating intermixed Ag-Cu nanoparticles used alternate pulsed laser ablation and deposition in an amorphous Al$_2$O$_3$ matrix.\cite{gonzalo:5163} Surface plasmon resonance (SPR) of bimetallic core-shell structures typically show two distinct resonance peaks where mixed particles show a single shifted and broadened resonance.\cite{Hodak:2000rb} The SPR for pure silver occurs at 400 nm and for copper at 570 nm.\cite{HengleinA._jp992950g} On Al$_2$O$_3$ films, these resonances move to 424 nm and 572 nm for the pure metals. For bimetallic nanoparticles with 40\% Ag an absorption peak is seen between 400-550 nm. With increasing Ag content, the SPR shifts towards the blue, with the peaks nearly coincident at a composition of 57\% Ag. Gonzalo {\it et al.} cited the existence of a single broad resonance peak as evidence of a mixed alloy particle rather than a phase segregated system. It should be noted that spectroscopy is a poor characterization technique for determining the the structure in nanoparticles. Characterization by high-resolution electron microscopy was unable to determine whether the mixed nanoparticles were an amorphous phase or a supersaturated crystalline phase. |
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Characterization of glassy behavior by molecular dynamics simulations |
| 131 |
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is typically done using dynamic measurements such as the mean squared |
| 132 |
> |
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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|
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< |
Characterization of glassy behavior by molecular dynamics simulations is typically done using dynamic measurements such as the mean squared displacement, $\langle r^2(t) \rangle$. Liquids exhibit a mean squared displacement that is linear in time (at long times). Glassy materials deviate significantly from this linear behavior at intermediate times, entering a sub-linear regime with a return to linear behavior in the infinite time limit.\cite{Kob:1999fk} However, diffusion in nanoparticles differs significantly from the bulk in that atoms are confined to a roughly spherical volume and cannot explore any region larger than the particle radius ($R$). In these confined geometries, $\langle r^2(t) \rangle$ approaches a limiting value of $3R^2/40$.\cite{ShibataT._ja026764r} This limits the utility of 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 |
| 146 |
> |
configurations). Local icosahedral structures are the |
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three-dimensional equivalent of covering a two-dimensional plane with |
| 148 |
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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 |
| 151 |
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order parameter that is sensitive to icosahedral |
| 152 |
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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 |
| 154 |
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solutions.\cite{wolde:9932} |
| 155 |
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|
| 156 |
< |
However, glassy materials exhibit strong icosahedral ordering among nearest-neghbors (in contrast with crystalline and liquid-like configurations). Local icosahedral structures are the three-dimensional equivalent of covering a two-dimensional plane with 5-sided tiles; they cannot be used to tile space in a periodic fashion, and are therefore an indicator of non-periodic packing in amorphous solids. Steinhart {\it et al.} defined an orientational bond order parameter that is sensitive to icosahedral ordering.\cite{Steinhardt:1983mo} This bond order parameter can therefore be used to characterize glass formation in liquid and solid solutions.\cite{wolde:9932} |
| 156 |
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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 |
| 162 |
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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 |
| 164 |
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was obtained from pair correlation functions, common neighbor analysis |
| 165 |
> |
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 |
| 168 |
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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 |
| 170 |
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amorphous structures in bulk materials. |
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|
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< |
Theoretical molecular dynamics studies have been performed on the formation of amorphous single component nanoclusters of either gold,\cite{Chen:2004ec,Cleveland:1997jb,Cleveland:1997gu} or nickel,\cite{Gafner:2004bg,Qi:2001nn} by rapid cooling($\thicksim 10^{12}-10^{13}$ K/s) from a liquid state. All of these studies found icosahedral ordering in the resulting structures produced by this rapid cooling which can be evidence of the formation of an amorphous structure.\cite{Strandburg:1992qy} The nearest neighbor information was obtained from pair correlation functions, common neighbor analysis and bond order parameters.\cite{Steinhardt:1983mo} It should be noted that these studies used single component systems with cooling rates that are only obtainable in computer simulations and particle sizes less than 20\AA. Single component systems are known to form amorphous states in small clusters,\cite{Breaux:rz} but do not generally form amorphous structures in bulk materials. |
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Since the nanoscale Ag-Cu alloy has been largely unexplored, many |
| 173 |
> |
interesting questions remain about the formation and properties of |
| 174 |
> |
such a system. Does the large surface area to volume ratio aid Ag-Cu |
| 175 |
> |
nanoparticles in rapid cooling and formation of an amorphous state? |
| 176 |
> |
Nanoparticles have been shown to have a size dependent melting |
| 177 |
> |
transition ($T_m$),\cite{Buffat:1976yq,Dick:2002qy} so we might expect |
| 178 |
> |
a similar trend to follow for the glass transition temperature |
| 179 |
> |
($T_g$). By analogy, bulk metallic glasses exhibit a correlation |
| 180 |
> |
between $T_m$ and $T_g$ although such dependence is difficult to |
| 181 |
> |
establish because of the dependence of $T_g$ on cooling rate and the |
| 182 |
> |
process by which the glass is formed.\cite{Wang:2003fk} It has also |
| 183 |
> |
been demonstrated that there is a finite size effect depressing $T_g$ |
| 184 |
> |
in polymer glasses in confined geometries.\cite{Alcoutlabi:2005kx} |
| 185 |
|
|
| 186 |
< |
Since the nanoscale Ag-Cu alloy has been largely unexplored, many interesting questions remain about the formation and properties of such a system. Does the large surface area to volume ratio aid Ag-Cu nanoparticles in rapid cooling and formation of an amorphous state? Would a predisposition to isosahedral ordering in nanoparticles also allow for easier formation of an amorphous state and what is the preferred ordering in a amorphous nanoparticle? Nanoparticles have been shown to have size dependent melting transition ($T_m$), so we would expect a similar trend to follow for the glass transition temperature ($T_g$).\cite{Buffat:1976yq,Dick:2002qy} By analogy, bulk metallic glasses exhibit a correlation between $T_m$ and $T_g$ although such dependence is difficult to establish because of the dependence of $T_g$ on cooling rate and the process by which the glass is formed.\cite{Wang:2003fk} It is also been demonstrated that there is a finite size effect depressing $T_g$ in polymer glasses in confined geometries.\cite{Alcoutlabi:2005kx} |
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|
| 188 |
< |
|
| 189 |
< |
In the sections below, we describe our modeling of the laser excitation and subsequent cooling of the particles {\it in silico} to mimic real experimental conditions. The simulation parameters have been tuned to the degree possible to match experimental conditions, and we discusss both the icosahedral ordering in the system, as well as the clustering of icosahedral centers that we observed. |
| 186 |
> |
In the sections below, we describe our modeling of the laser |
| 187 |
> |
excitation and subsequent cooling of the particles {\it in silico} to |
| 188 |
> |
mimic real experimental conditions. The simulation parameters have |
| 189 |
> |
been tuned to the degree possible to match experimental conditions, |
| 190 |
> |
and we discusss both the icosahedral ordering in the system, as well |
| 191 |
> |
as the clustering of icosahedral centers that we observed. |
