


Using Xray fine structure absorption spectroscopy
(XAFS), the Bunker group in the department of Physics
observed that goldcore / silvershell nanoparticles
in aqueous solution at ambient temperature form an
alloy near the interface between the two metals.[2] The amount of interdiffusion is
highly dependent on the size of the nanoparticle
core with larger cores alloying on a
substantially slower time scale. This alloying occurs
with a timescale of approximately three days (which is
79 orders of magnitude too fast to be
explained by normal solidstate diffusion). Diffusion
of atoms in a liquid droplet would cause the entire
particle to alloy in a few microseconds. Our group
along with the Meisel group of the Notre Dame
Radiation Laboratory and the Bunker group, we have
helped to explain this phenomenon. Our calculations
show that the fast alloying times are due to vacancies
present at the interface layer between the two
metals. To gain insight into the alloying mechanism, molecular dynamics simulations were carried out on nanoparticles composed of Ag and Au atoms interacting under the Embedded Atom Method (EAM) potential. [3] Gold and silver have nearly identical lattice constants, so the nanoparticles were constructed on a perfect FCC lattice using a lattice constant of 4.085 Å. Gold atoms were placed inside of the core radius (r_{core}) and silver atoms were filled in out to the particle radius (r_{shell} ). We designated a 2 Å "interface" region centered on r_{core} where either 5% or 10% of the interfacial atoms were removed at random for the simulations that involved vacancies. For these simulations, r_{core} = 1.25 nm and r_{shell} = 1.998 nm matching the smallest of the nanoparticles studied by our collaborators. Before starting the molecular dynamics simulations, a relatively short steepestdescent minimization was performed to relax the lattice in the initial configuration. During the initial 30 ps of each trajectory, velocities were repeatedly sampled from a MaxwellBoltzmann distribution matching the target temperature for the run. Following this initialization procedure, trajectories were run in the microcanonical (constantNVE) ensemble with zero initial total angular momentum. In order to compare the structural features obtained from the NVEensemble molecular dynamics, additional trajectories were run using a modified NoséHoover thermostat to maintain constant temperature (NVT) and zero total angular momentum. Data collection for all of the simulations started after the 30 ps equilibration period had been completed. We simulated particles with the abovementioned interfacial vacancy density at 100 K intervals from 500 to 1200 K. Given the masses of the constituent atoms, we were able to use time steps of 5 fs while maintaining excellent energy conservation. Typical simulation times were 100 ns for nanoparticles simulated at 500600 K and 1224 ns for particles at 6001200 K. From simulation results, we have constructed a radial density profile of the two constituents as a function of distance from the center of the nanoparticle. This density profile was obtained from the last 2 ns of the 24 ns simulations at 800 K. Remarkably, the interfacial vacancies result in a substantial smoothing of the peaks in the density profile, indicating that those nanoparticles are closer to the melting transition. The region near 1.25 nm in the radial density profile shows the interfacial vacancies result in significantly enhanced radial diffusion of the Ag into the core region. Much of the displacement occurs along the interface (i.e., at constant r) which can be seen from the broadening of the density peaks. 

Atoms confined to a spherical volume of radius R have
a mean square displacement the approaches
6R^{2}/5 in the infinite time limit. (In bulk
systems, the mean squared displacement is unbounded
and can grow linearly with time.) At short times, a
useful approach might be to connect the observable
displacements of atoms in the simulation to solutions
of the appropriate diffusion equation. For a
spherically symmetric volume and reflecting boundary
conditions at R, the solutions to the diffusion
equation are given by
where the coefficients a_{n} are determined by the initial displacements of the atoms. Proper mapping of the displacements of the individual atoms would require projecting initial and final positions of each atom onto the diffusional modes expressed in the summation. An alternative approach is to compute the relaxation time of the mean squared displacement using the correct infinite time limit and the KohlraushWilliamWatts (KWW) relaxation law, [4] 
Nanoparticles exhibit behavior not displayed in the
bulk because of a high surface area to volume
ratio. Energy due to photons absorbed during ultrafast
laser excitation is transfered into thermal excitation
of atomic degrees of freedom, coherently exiting the
breathing mode of the nanoparticle. Dephasing of this
breathing mode has been seen in laser experiments by
Greg Hartland's group of the Department of Chemistry
and Biochemsitry. [6] Dephasing
following the coherent excitation of the breathing
mode may be due to inhomogeneous size distributions in
the sample, but may also be due to softening of the
breathing mode vibrational frequency following a
melting transition. We have performed molecular
dynamics simulations that mimic the laser excitation
experiments of Hartland's lab to gain insight into the
possible mechanism for this breathing mode
dephasing. [7] Spherical Au nanoparticles were created from the bulk in a standard FCC latice at four different radii [20 Å (1926 atoms), 20 Å (6602 atoms) and 35 Å (10606 atoms)] using a lattice spacing of 4.08 Å. Potentials for the Au interactions were once again provided by the EAM model. The ultrafast laser excitation event was modeled by sampling from a Boltzmann Distribution at twice the target temperature. Following the excitation event, nanoparticles evolved in a canonical ensemble using NoséHoover NVT at the target temperature for 40 ps. Five independent samples with target temperature spanning a range from 300 K to 1350 K were studied. Volume was determined as a function of time by using the convex hull geometric construction which defines the smallest convex polyhedron which include all of the atoms as calculated by the Quickhull algorithm. [8] From these simulations, we find that there is both a size and temperaturedependent softening of these nanoparticles even at temperatures below the melting temperature. In a plot of the Bulk Modulus (K) for the various size nanoparticles studied as a function of final temperature after excitation, we can see a dramatic (and sizedependent) drop in K at temperature well below the melting temperature of bulk polycrystalline gold. (Polycrystalline gold has a bulk modulus of 220 GPa at a temperature of 300 K.) Surface melting occurs at even lower temperatures as indicated by our calculations of the radialdensity profile which shows a merging of the crystalline peaks in the outer layer of the nanoparticle much like that seen in the AgAu nanoparticle with vacancies. The timedependent estimate for the bulk modulus indicates a time scale for softening of about 10 ps independent of particle size. Correspondingly, the smaller particles exhibit coherent breathing vibrations for a few periods before melting and larger particles melt within the first vibrational period. 

In our study of the laser excitation of gold
nanoparticles, we observed that the cooling rate for
these particles (10^{11}10 ^{12} K/s)
which is in excess of the cooling rate required for
glass formation in bulk metal alloys. We believe that
it may be feasible to use laser excitation to melt,
alloy and quench a metallic nanoparticle in order to
form a metallic glass nanobead. 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. [9] We have modeled the laser
excitation and cooling by constructing and relaxing
the eutectic composition
(Ag_{6}Cu_{4}) on a FCC lattice with a
lattice constant of 4.09 Å for 20, 30 and 40
Å radius nanoparticles. The nanoparticles are
melted at 900 K and allowed to mix for 1 ns. Resulting
structures are then quenched using a implicit solvent
model where Langevin dynamics is applied to the outer
4 Å radius of the nanoparticle and normal
Newtonian dynamics are applied to the rest of the
atoms. By fitting to experimentallydetermined cooling
rates, we find that collision frequencies of 3.58
fs^{1} for Ag and 5.00 fs^{1} for Cu
lead to nearly exact agreement with the Temperature
vs. time data. The cooling rates are therefore 2.37 x
10^{13} K/s, 1.37 x 10^{13} K/s and
1.06 x 10^{13} K/s for the 20, 30 and 40
Å radius nanoparticles respectively. Structural Measures for Glass Formation Characterization of glassy behavior by molecular dynamics simulations is typically done using dynamic measurements such as the mean squared displacement, <r^{2}(t)>. Liquids exhibit a mean squared displacement that is linear in time. Glassy materials deviate significantly from this linear behavior at intermediate times, entering a sublinear regime with a return to linear behavior in the infinite time limit. 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. In these confined geometries, <r^{2}(t)> in the radial direction approaches a limiting value of 6R^{2}/40. However, glassy materials exhibit strong icosahedral ordering among nearestneghbors in contrast to crystalline or liquid structures. Steinhart, et al., defined an orientational bond order parameter that is sensitive to the nearestneighbor environment by using invariant combinations of spherical harmonics Y_{l,m}(θ,φ).[10] Spherical harmonics involving the Y_{6,m}(θ,φ) are particularly sensitive to icosohedral order among nearest neighbors as can be seen in the cartoon to the left. The second and thirdorder invariants, Q_{6} and W_{6} 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 Q_{6} and 0.170 for W_{6}. A plot of the distributions of Q_{6} and W_{6} 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. 

References [1] Meineke M. A.; Vardeman II, C. F.; Lin T.; Fennell C. J.; Gezelter J. D. J. Comp. Chem., 2005 26, 252. [2] Shibata T.; Bunker B.A.; Zhang Z.; Meisel D.; Vardeman II C. F.; Gezelter J. D. J. Am. Chem. Soc., 2002 124, 11989. [3] Foiles S. M.; Baskes M. I.; Daw M. S. Phys. Rev. B, 1986, 33, 7983 [4] Williams G.; Watts D. C. Trans. Faraday Soc., 1970, 66, 80. [5] Tu, K.N.; Mayer, J. W. Electronic Thin Film Science; Macmillan: New York, 1992. [6] Hartland, G. V.; Hu, M.; Sader, J. E. J. Phys. Chem. B, 2003, 107, 7472 [7] Vardeman II, C. F.; Conforti, P. F.; Sprague, M. M.; Gezelter, J. D. J. Phys. Chem. B, 2005, 109, 16695 [8] Qhull, 1993. Software library is available from the National Science and Technology Research Center for Computation and Visualization of Geometric Structures, University of Minnesota. http://www.qhull.org [9] Vardeman II, C. F.; Gezelter, J. D. J. Phys. Chem. A, 2001, 105, 2568 [10] Steinhardt, P. J.; Nelson, D. R.; Ronchetti, M. Phys. Rev. B, 1982, 28, 784 