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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 |
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groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003yf,HuM._jp020581+,plech:195423} |
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They have [BRIEF SURVEY OF THE EXPERIMENTAL WORK] |
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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{} 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{Vardeman2001} |
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XXX stuff from ORP |
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In the sections below, we describe our |
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modeling of the laser excitation and subsequent cooling of the |
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particles in silico to mimic real experimental conditions. |
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constructing and relaxing the eutectic composition (Ag$_6$Cu$_4$) on a |
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FCC lattice with a lattice constant of 4.09 \AA\ for 20, 30 and 40 |
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\AA\ radius nanoparticles. The nanoparticles are melted at 900 K and |
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allowed to mix for 1 ns. Resulting structures are then quenched using |
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a implicit solvent model where Langevin dynamics is applied to the |
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outer 4 \AA\ radius of the nanoparticle and normal Newtonian dynamics |
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are applied to the rest of the atoms. By fitting to |
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experimentally-determined cooling rates, we find that collision |
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frequencies of 3.58 fs$^-1$ for Ag and 5.00 fs$^-1$ for Cu lead to |
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nearly exact agreement with the Temperature vs. time data. The cooling |
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rates are therefore 2.37 x 10$^13$ K/s, 1.37 x 10$^13$ K/s and 1.06 x |
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10$^13$ K/s for the 20, 30 and 40 \AA\ radius nanoparticles |
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respectively. |
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Structural Measures for Glass Formation |
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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, <r2(t)>. Liquids exhibit a mean squared displacement |
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that is linear in time. Glassy materials deviate significantly from |
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this linear behavior at intermediate times, entering a sub-linear |
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regime with a return to linear behavior in the infinite time |
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limit. Diffusion in nanoparticles differs significantly from the bulk |
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in that atoms are confined to a roughly spherical volume and cannot |
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explore any region larger than the particle radius. In these confined |
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geometries, <r2(t)> in the radial direction approaches a limiting |
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value of 6R2/40. |
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However, glassy materials exhibit strong icosahedral ordering among nearest-neghbors in contrast to crystalline or liquid structures. Steinhart, et al., defined an orientational bond order parameter that is sensitive to the nearest-neighbor environment by using invariant combinations of spherical harmonics Yl,m(?,?).[10] Spherical harmonics involving the Y6,m(?,?) are particularly sensitive to icosohedral order among nearest neighbors as can be seen in the cartoon to the left. The second and third-order invariants, Q6 and W6 are used to determine the level of icosahedral order present in a quenched nanoparticle. Perfect icosahedral structures have a maximal value of 0.663 for Q6 and -0.170 for W6. A plot of the distributions of Q6 and W6 with cooling temperature indicates increasing icosahedral order with decreasing temperature. This is a clear indication that glassy structures are forming as the nanoparticles are quenched. |
