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\contentsline {figure}{\numberline {1.1}{\ignorespaces General shape of the pair interaction energy between molecules where $-\epsilon $ is the minimum energy, $\sigma $ is the close interaction distance and $R_m$ is the minimum energy separation.}}{8}{figure.1.1} |
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\contentsline {figure}{\numberline {1.2}{\ignorespaces Functional Forms for {\sc EAM} Parameters.}}{16}{figure.1.2} |
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\contentsline {figure}{\numberline {2.1}{\ignorespaces Radial distribution functions for Ag$_6$Cu$_4$. The appearance of the split second peak at 500 K indicates the onset of a structural change in the super-cooled liquid at temperatures above $T_{g}$.}}{41}{figure.2.1} |
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\contentsline {figure}{\numberline {2.2}{\ignorespaces Wendt-Abraham parameter ($R_{WA}$) as a function of temperature. $T^{WA}_{g} \approx $ 540 K for a cooling rate of $1.56 \times 10^{11}$ K/s.}}{43}{figure.2.2} |
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\contentsline {figure}{\numberline {2.3}{\ignorespaces Density of states calculated from quenched normal modes, $\rho _q(\omega )$, and from the Fourier transform of the velocity autocorrelation function $\rho _o(\omega )$.}}{44}{figure.2.3} |
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\contentsline {figure}{\numberline {2.4}{\ignorespaces Arrhenius plot of the self-diffusion constants indicating significant deviation from Arrhenius behavior at temperatures below 450 K.}}{46}{figure.2.4} |
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\contentsline {figure}{\numberline {2.5}{\ignorespaces Self-Diffusion constant for the two models under consideration compared to the values computed via standard techniques.}}{48}{figure.2.5} |
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\contentsline {figure}{\numberline {2.6}{\ignorespaces {\sc ctrw} hopping distance, $\sigma _0(T)$, as a function of temperature assuming $\gamma =1$ and using the cage correlation hopping times.}}{49}{figure.2.6} |
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\contentsline {figure}{\numberline {2.7}{\ignorespaces Comparison of exponential stretching coefficients, $\beta $ from the cage-correlation function and $\gamma $ from CTRW theory.}}{50}{figure.2.7} |
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\contentsline {figure}{\numberline {2.8}{\ignorespaces The characteristic hopping time, $\tau _{hop}$, which characterizes the waiting time distribution. The solid circles represent hopping times predicted from {\sc kww} fits to the cage-correlation function. The open triangles represent the characteristic time calculated via the {\sc ctrw} model for $\delimiter "426830A r^{2}(t) \delimiter "526930B $.}}{51}{figure.2.8} |
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\contentsline {figure}{\numberline {3.1}{\ignorespaces Methodology for Molecular Dynamics simulations. Atoms were removed at random from the 2 \r A\ region surrounding the core-shell interface.}}{59}{figure.3.1} |
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\contentsline {figure}{\numberline {3.2}{\ignorespaces Cross Section of Model Used for Simulations. Vacancies at the Interface are Represented by the Red Translucent Spheres.}}{60}{figure.3.2} |
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\contentsline {figure}{\numberline {3.3}{\ignorespaces Arrhenius plot of relaxation times for the particles of Figure \ref {nanodiff:fig:vacancy_dens} in the absence (triangles) and presence of 10\% (circles) vacancies, taken from fits of the mean square displacements of the atoms vs. time.}}{63}{figure.3.3} |
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\contentsline {figure}{\numberline {3.4}{\ignorespaces Density profiles of Au and Ag atoms within the NP during the last 2 ns of a 24 ns NVE simulation. Solid profile: no interfacial vacancies. Dotted profile: 10\% initial interfacial vacancies.}}{64}{figure.3.4} |
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\contentsline {figure}{\numberline {4.1}{\ignorespaces Comparison of two of the methods for estimating the bulk modulus as a function of temperature for the 35\r A\ particle.}}{73}{figure.4.1} |
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\contentsline {figure}{\numberline {4.2}{\ignorespaces The temperature dependence of the bulk modulus (upper panel) and heat capacity (lower panel) for nanoparticles of four different radii. Note that the peak in the heat capacity coincides with the {\em start} of the peak in the bulk modulus.}}{75}{figure.4.2} |
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\contentsline {figure}{\numberline {4.3}{\ignorespaces The dependence of the spike in the heat capacity on the length of the simulation. Longer heating-response calculations result in melting transitions that are sharper and lower in temperature than the short-time transient response simulations. Shorter runs don't allow the particles to melt completely.}}{76}{figure.4.3} |
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\contentsline {figure}{\numberline {4.4}{\ignorespaces Sample Volume traces for the 20 \r A\ and 35 \r A\ particles at a range of temperatures. Note the relatively rapid ($<$ 10 ps) decoherence due to melting in the 20 \r A\ particle as well as the difference between the 1100 K and 1200 K traces in the 35 \r A\ particle.}}{77}{figure.4.4} |
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\contentsline {figure}{\numberline {4.5}{\ignorespaces Volume fluctuation autocorrelation functions for the 20 \r A\ (lower panel) and 35 \r A\ (upper panel) particles at a range of temperatures. Successive temperatures have been translated upwards by one unit. Note the beat pattern in the 20 \r A\ particle at 800K.}}{78}{figure.4.5} |
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\contentsline {figure}{\numberline {4.6}{\ignorespaces The temperature dependence of the period of the breathing mode for the four different nanoparticles studied in this work.}}{79}{figure.4.6} |
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\contentsline {figure}{\numberline {5.1}{\ignorespaces Methodology used to mimic the experimental cooling conditions of a hot nanoparticle surrounded by a solvent. Atoms in the core of the particle evolved under Newtonian dynamics, while atoms that were in the outer skin of the particle evolved under Langevin dynamics. The radius of the spherical region operating under Newtonian dynamics, $r_\textrm {Newton}$ was set to be 4 {\r A} smaller than the original radius ($R$) of the liquid droplet.}}{92}{figure.5.1} |
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\contentsline {figure}{\numberline {5.2}{\ignorespaces Thermal cooling curves obtained from the inverse Laplace transform heat model in Eq. (\ref {eq:laplacetransform}) (solid line) as well as from molecular dynamics simulations (circles). Effective solvent viscosities of 4.2-7.5 $\times 10^{-6}$ Pa s (depending on the radius of the particle) give the best fit to the experimental cooling curves. This viscosity suggests that the nanoparticles in these experiments are surrounded by a vapor layer (which is a reasonable assumption given the initial temperatures of the particles). }}{96}{figure.5.2} |
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\contentsline {figure}{\numberline {5.3}{\ignorespaces Illustrative cooling profile for the 40 {\r A} nanoparticle evolving under stochastic boundary conditions corresponding to $G=$$87.5\times 10^{6}$ $(\mathrm {Wm^{-2}K^{-1}})$.}}{97}{figure.5.3} |
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\contentsline {figure}{\numberline {5.4}{\ignorespaces Cutaway views of 30 \r A\ Ag-Cu nanoparticle structures for random alloy (top) and Cu (core) / Ag (shell) initial conditions (bottom). Shown from left to right are the crystalline, liquid droplet, and final glassy bead configurations.}}{98}{figure.5.4} |
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\contentsline {figure}{\numberline {5.5}{\ignorespaces Distributions of the bond orientational order parameter ($\mathaccentV {hat}05E{W}_6$) at different temperatures (colors). The upper, middle, and lower panels are for 20, 30, and 40 \r A\ particles, respectively. The left-hand column used cooling rates commensurate with a low interfacial conductance ($87.5 \times 10^{6}$ $\mathrm {Wm^{-2}K^{-1}}$), while the right-hand column used a more physically reasonable value of $117 \times 10^{6}$ $\mathrm {Wm^{-2}K^{-1}}$. The peak at $\mathaccentV {hat}05E{W}_6 \approx -0.17$ is due to local icosahedral structures. The different curves in each of the panels indicate the distribution of $\mathaccentV {hat}05E{W}_6$ values for samples taken at different times along the cooling trajectory. The initial and final temperatures (in K) are indicated on the plots adjacent to their respective distributions.}}{103}{figure.5.5} |
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\contentsline {figure}{\numberline {5.6}{\ignorespaces Distributions of the bond orientational order parameter ($Q_6$) at different temperatures (colors). The curves in the six panels in this figure were computed at identical conditions to the same panels in figure \ref {fig:w6}.}}{104}{figure.5.6} |
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\contentsline {figure}{\numberline {5.7}{\ignorespaces Free energy as a function of the orientational order parameter ($\mathaccentV {hat}05E{W}_6$) for 40 {\r A} bimetallic nanoparticles as they are cooled from 902 K to 310 K. As the particles cool below 528 K, a local minimum in the free energy surface appears near the perfect icosahedral ordering ($\mathaccentV {hat}05E{W}_6 = -0.17$). At all temperatures, liquid-like structures are a global minimum on the free energy surface, but if the cooling rate is fast enough, substructures may become trapped with local icosahedral order, leading to the formation of a glass.}}{106}{figure.5.7} |
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\contentsline {figure}{\numberline {5.8}{\ignorespaces Temperature dependence of the fraction of atoms with local icosahedral ordering, $f_\textrm {icos}(T)$ for 20, 30, and 40 \r A\ particles cooled at two different values of the interfacial conductance.}}{107}{figure.5.8} |
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\contentsline {figure}{\numberline {5.9}{\ignorespaces Distributions of the bond orientational order parameter ($\mathaccentV {hat}05E{W}_6$) for the two different elements present in the nanoparticles. This distribution was taken from the fully-cooled 40 \r A\ nanoparticle. Local icosahedral ordering around copper atoms is much more prevalent than around silver atoms.}}{108}{figure.5.9} |
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\contentsline {figure}{\numberline {5.10}{\ignorespaces Centers of local icosahedral order ($\mathaccentV {hat}05E{W}_6<0.15$) at 900 K, 471 K and 315 K for the 30 \r A\ nanoparticle cooled with an interfacial conductance $G = 87.5 \times 10^{6}$ $\mathrm {Wm^{-2}K^{-1}}$. Silver atoms (blue) exhibit icosahedral order at the surface of the nanoparticle while copper icosahedral centers (green) are distributed throughout the nanoparticle. The icosahedral centers appear to cluster together and these clusters increase in size with decreasing temperature.}}{110}{figure.5.10} |
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\contentsline {figure}{\numberline {5.11}{\ignorespaces Appearance of icosahedral clusters around central silver atoms is largely due to the presence of these silver atoms at or near the surface of the nanoparticle. The upper panel shows the fraction of icosahedral atoms ($f_\textrm {icos}(r)$ for each of the two metallic atoms as a function of distance from the center of the nanoparticle ($r$). The lower panel shows the radial density of the two constituent metals (relative to the overall density of the nanoparticle). Icosahedral clustering around copper atoms are more evenly distributed throughout the particle, while icosahedral clustering around silver is largely confined to the silver atoms at the surface.}}{112}{figure.5.11} |
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\contentsline {figure}{\numberline {6.1}{\ignorespaces Implicit Constant Pressure Langevin Bath(blue) Coupled with Explict Water and Metallic Nanoparticle.}}{117}{figure.6.1} |
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\contentsline {figure}{\numberline {6.2}{\ignorespaces Method for Computing Constant Pressure Forces on Surface Atoms in a Nanoparticle Using the Convex Hull.}}{119}{figure.6.2} |
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\contentsline {figure}{\numberline {6.3}{\ignorespaces Constant Pressure Langevin Dynamics $P_{int}$ vs Normalized Volume $V/V_{eq}$ for a 1926 atom Au nanoparticle using the {\sc QSC} potential (\ref {introSec:tightbind}) measured at 301 K.}}{120}{figure.6.3} |
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\contentsline {figure}{\numberline {6.4}{\ignorespaces Orientation of water molecules relative to Au surface. The correct orientation as calculated by DFT(Top) and the classical Spohr model (Bottom).}}{122}{figure.6.4} |
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\contentsline {figure}{\numberline {6.5}{\ignorespaces The $1b_1$ HOMO in water as calculated by Gaussian 03 using the B3LYP/6-311+G(d,p) level of theory.}}{123}{figure.6.5} |
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\contentsline {figure}{\numberline {6.6}{\ignorespaces Coordinate reference frame for the orientational water-metal model. }}{124}{figure.6.6} |
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