trunk/nanoglass/introduction.tex



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\section{Introduction}

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 particle, resulting in a
rapid heating of the lattice of the metal particles.  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
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.\cite{Mafune01,HartlandG.V._jp0276092,Link:2000lr,Plech:2003yq,plech:195423,Plech:2007rt}

Much of the experimental work on this subject has been carried out in
the Hartland, El-Sayed and Plech
groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003lr,Petrova:2007qy,Link:2000lr,plech:195423,Plech:2007rt}
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.  This is in agreement with Cahill,\cite{Wilson:2002uq}
but opposite to the conclusions in Reference \citen{Hu:2004lr}.

Since these experiments are carried out in condensed phase
surroundings, the large surface area to volume ratio makes the heat
transfer to the surrounding solvent 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.\cite{Greer:1995qy} Given this fact, it may be
possible to use laser excitation to melt, alloy and quench metallic
nanoparticles in order to form glassy nanobeads.

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}

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.

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.

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 an alloyed
particle rather than a phase segregated system.  However, spectroscopy
may not be able to tell the difference between alloyed particles and
mixtures of segregated particles.  High-resolution electron microscopy
has so far been unable to determine whether the mixed nanoparticles
were an amorphous phase or a supersaturated crystalline phase.

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.

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}

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.

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?
Nanoparticles have been shown to have a size dependent melting
transition ($T_m$),\cite{Buffat:1976yq,Dick:2002qy} so we might expect
a similar trend to follow for the glass transition temperature
($T_g$). 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 has also
been demonstrated that there is a finite size effect depressing $T_g$
in polymer glasses in confined geometries.\cite{Alcoutlabi:2005kx}

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.
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3	%!TEX root = /Users/charles/Desktop/nanoglass/nanoglass.tex
4
5	\section{Introduction}
6
7	Excitation of the plasmon resonance in metallic nanoparticles has
8	attracted enormous interest in the past several years. This is partly
9	due to the location of the plasmon band in the near IR for particles
10	in a wide range of sizes and geometries. Living tissue is nearly
11	transparent in the near IR, and for this reason, there is an
12	unrealized potential for metallic nanoparticles to be used in both
13	diagnostic and therapeutic settings.\cite{West:2003fk,Hu:2006lr} One
14	of the side effects of absorption of laser radiation at these
15	frequencies is the rapid (sub-picosecond) heating of the electronic
16	degrees of freedom in the metal. This hot electron gas quickly
17	transfers heat to the phonon modes of the particle, resulting in a
18	rapid heating of the lattice of the metal particles. Since metallic
19	nanoparticles have a large surface area to volume ratio, many of the
20	metal atoms are at surface locations and experience relatively weak
21	bonding. This is observable in a lowering of the melting temperatures
22	of these particles when compared with bulk metallic
23	samples.\cite{Buffat:1976yq,Dick:2002qy} One of the side effects of
24	the excitation of small metallic nanoparticles at the plasmon
25	resonance is the facile creation of liquid metal
26	droplets.\cite{Mafune01,HartlandG.V._jp0276092,Link:2000lr,Plech:2003yq,plech:195423,Plech:2007rt}
27
28	Much of the experimental work on this subject has been carried out in
29	the Hartland, El-Sayed and Plech
30	groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003lr,Petrova:2007qy,Link:2000lr,plech:195423,Plech:2007rt}
31	These experiments mostly use the technique of time-resolved optical
32	pump-probe spectroscopy, where a pump laser pulse serves to excite
33	conduction band electrons in the nanoparticle and a following probe
34	laser pulse allows observation of the time evolution of the
35	electron-phonon coupling. Hu and Hartland have observed a direct
36	relation between the size of the nanoparticle and the observed cooling
37	rate using such pump-probe techniques.\cite{Hu:2004lr} Plech {\it et
38	al.} have use pulsed x-ray scattering as a probe to directly access
39	changes to atomic structure following pump
40	excitation.\cite{plech:195423} They further determined that heat
41	transfer in nanoparticles to the surrounding solvent is goverened by
42	interfacial dynamics and not the thermal transport properties of the
43	solvent. This is in agreement with Cahill,\cite{Wilson:2002uq}
44	but opposite to the conclusions in Reference \citen{Hu:2004lr}.
45
46	Since these experiments are carried out in condensed phase
47	surroundings, the large surface area to volume ratio makes the heat
48	transfer to the surrounding solvent a relatively rapid process. In our
49	recent simulation study of the laser excitation of gold
50	nanoparticles,\cite{VardemanC.F._jp051575r} we observed that the
51	cooling rate for these particles (10$^{11}$-10$^{12}$ K/s) is in
52	excess of the cooling rate required for glass formation in bulk
53	metallic alloys.\cite{Greer:1995qy} Given this fact, it may be
54	possible to use laser excitation to melt, alloy and quench metallic
55	nanoparticles in order to form glassy nanobeads.
56
57	To study whether or not glass nanobead formation is feasible, we have
58	chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a
59	model system because it is an experimentally known glass former, and
60	has been used previously as a theoretical model for glassy
61	dynamics.\cite{Vardeman-II:2001jn} The Hume-Rothery rules suggest that
62	alloys composed of Copper and Silver should be miscible in the solid
63	state, because their lattice constants are within 15\% of each
64	another.\cite{Kittel:1996fk} Experimentally, however Ag-Cu alloys are
65	a well-known exception to this rule and are only miscible in the
66	liquid state given equilibrium conditions.\cite{Massalski:1986rt}
67	Below the eutectic temperature of 779 $^\circ$C and composition
68	(60.1\% Ag, 39.9\% Cu), the solid alloys of Ag and Cu will phase
69	separate into Ag and Cu rich $\alpha$ and $\beta$ phases,
70	respectively.\cite{Banhart:1992sv,Ma:2005fk} This behavior is due to a
71	positive heat of mixing in both the solid and liquid phases. For the
72	one-to-one composition fcc solid solution, $\Delta H_{\rm mix}$ is on
73	the order of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid
74	solutions may be formed by undercooling, and under these conditions, a
75	compositionally-disordered $\gamma$ fcc phase can be
76	formed.\cite{najafabadi:3144}
77
78	Metastable alloys composed of Ag-Cu were first reported by Duwez in
79	1960 and were created by using a ``splat quenching'' technique in
80	which a liquid droplet is propelled by a shock wave against a cooled
81	metallic target.\cite{duwez:1136} Because of the small positive
82	$\Delta H_{\rm mix}$, supersaturated crystalline solutions are
83	typically obtained rather than an amorphous phase. Higher $\Delta
84	H_{\rm mix}$ systems, such as Ag-Ni, are immiscible even in liquid
85	states, but they tend to form metastable alloys much more readily than
86	Ag-Cu. If present, the amorphous Ag-Cu phase is usually seen as the
87	minority phase in most experiments. Because of this unique
88	crystalline-amorphous behavior, the Ag-Cu system has been widely
89	studied. Methods for creating such bulk phase structures include splat
90	quenching, vapor deposition, ion beam mixing and mechanical
91	alloying. Both structural \cite{sheng:184203} and
92	dynamic\cite{Vardeman-II:2001jn} computational studies have also been
93	performed on this system.
94
95	Although bulk Ag-Cu alloys have been studied widely, this alloy has
96	been mostly overlooked in nanoscale materials. The literature on
97	alloyed metallic nanoparticles has dealt with the Ag-Au system, which
98	has the useful property of being miscible on both solid and liquid
99	phases. Nanoparticles of another miscible system, Au-Cu, have been
100	successfully constructed using techniques such as laser
101	ablation,\cite{Malyavantham:2004cu} and the synthetic reduction of
102	metal ions in solution.\cite{Kim:2003lv} Laser induced alloying has
103	been used as a technique for creating Au-Ag alloy particles from
104	core-shell particles.\cite{Hartland:2003lr} To date, attempts at
105	creating Ag-Cu nanoparticles have used ion implantation to embed
106	nanoparticles in a glass matrix.\cite{De:1996ta,Magruder:1994rg} These
107	attempts have been largely unsuccessful in producing mixed alloy
108	nanoparticles, and instead produce phase segregated or core-shell
109	structures.
110
111	One of the more successful attempts at creating intermixed Ag-Cu
112	nanoparticles used alternate pulsed laser ablation and deposition in
113	an amorphous Al$_2$O$_3$ matrix.\cite{gonzalo:5163} Surface plasmon
114	resonance (SPR) of bimetallic core-shell structures typically show two
115	distinct resonance peaks where mixed particles show a single shifted
116	and broadened resonance.\cite{Hodak:2000rb} The SPR for pure silver
117	occurs at 400 nm and for copper at 570 nm.\cite{HengleinA._jp992950g}
118	On Al$_2$O$_3$ films, these resonances move to 424 nm and 572 nm for
119	the pure metals. For bimetallic nanoparticles with 40\% Ag an
120	absorption peak is seen between 400-550 nm. With increasing Ag
121	content, the SPR shifts towards the blue, with the peaks nearly
122	coincident at a composition of 57\% Ag. Gonzalo {\it et al.} cited the
123	existence of a single broad resonance peak as evidence of an alloyed
124	particle rather than a phase segregated system. However, spectroscopy
125	may not be able to tell the difference between alloyed particles and
126	mixtures of segregated particles. High-resolution electron microscopy
127	has so far been unable to determine whether the mixed nanoparticles
128	were an amorphous phase or a supersaturated crystalline phase.
129
130	Characterization of glassy behavior by molecular dynamics simulations
131	is typically done using dynamic measurements such as the mean squared
132	displacement, $\langle r^2(t) \rangle$. Liquids exhibit a mean squared
133	displacement that is linear in time (at long times). Glassy materials
134	deviate significantly from this linear behavior at intermediate times,
135	entering a sub-linear regime with a return to linear behavior in the
136	infinite time limit.\cite{Kob:1999fk} However, diffusion in
137	nanoparticles differs significantly from the bulk in that atoms are
138	confined to a roughly spherical volume and cannot explore any region
139	larger than the particle radius ($R$). In these confined geometries,
140	$\langle r^2(t) \rangle$ approaches a limiting value of
141	$3R^2/40$.\cite{ShibataT._ja026764r} This limits the utility of
142	dynamical measures of glass formation when studying nanoparticles.
143
144	However, glassy materials exhibit strong icosahedral ordering among
145	nearest-neghbors (in contrast with crystalline and liquid-like
146	configurations). Local icosahedral structures are the
147	three-dimensional equivalent of covering a two-dimensional plane with
148	5-sided tiles; they cannot be used to tile space in a periodic
149	fashion, and are therefore an indicator of non-periodic packing in
150	amorphous solids. Steinhart {\it et al.} defined an orientational bond
151	order parameter that is sensitive to icosahedral
152	ordering.\cite{Steinhardt:1983mo} This bond order parameter can
153	therefore be used to characterize glass formation in liquid and solid
154	solutions.\cite{wolde:9932}
155
156	Theoretical molecular dynamics studies have been performed on the
157	formation of amorphous single component nanoclusters of either
158	gold,\cite{Chen:2004ec,Cleveland:1997jb,Cleveland:1997gu} or
159	nickel,\cite{Gafner:2004bg,Qi:2001nn} by rapid cooling($\thicksim
160	10^{12}-10^{13}$ K/s) from a liquid state. All of these studies found
161	icosahedral ordering in the resulting structures produced by this
162	rapid cooling which can be evidence of the formation of an amorphous
163	structure.\cite{Strandburg:1992qy} The nearest neighbor information
164	was obtained from pair correlation functions, common neighbor analysis
165	and bond order parameters.\cite{Steinhardt:1983mo} It should be noted
166	that these studies used single component systems with cooling rates
167	that are only obtainable in computer simulations and particle sizes
168	less than 20\AA. Single component systems are known to form amorphous
169	states in small clusters,\cite{Breaux:rz} but do not generally form
170	amorphous structures in bulk materials.
171
172	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	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.