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.)  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.

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 a substantial softening of the bulk modulus
of these particles when compared with bulk metallic samples.  One of
the side effects of the excitation of small metallic nanoparticles at
the plasmon resonance is the facile creation of liquid metal
droplets.  

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 the electron-phonon coupling to be observed as a function of time. 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{HuM._jp020581+} Pleach {\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. 


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 metallic glass
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. 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. 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, $\Delta H$ 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.

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
$\Delta H$, supersaturated crystalline solutions are typically
obtained rather than an amorphous phase. Higher $\Delta H$ 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 a mixed alloy particle rather than a
phase segregated system. Unfortunately, they were unable to determine
whether the mixed nanoparticles were an amorphous phase or a
supersaturated crystalline phase. One consequence of embedding the
Ag-Cu nanoparticles in a glass matrix is that the SPR can be shifted
because of the nanoparticle-glass matrix
interaction.\cite{De:1996ta,Roy:2003dy}

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 to crystalline or liquid structures.
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 a 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. Icosahedral structures have
also been reported in nanoparticles, particularly multiply twinned
particles.\cite{Ascencio:2000qy}

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 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,\cite{Buffat:1976yq} and we would expect a similar trend
to follow for the glass transition temperature.

In the sections below, we describe our modeling of the laser
excitation and subsequent cooling of the particles 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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1	%!TEX root = /Users/charles/Desktop/nanoglass/nanoglass.tex
2
3	\section{Introduction}
4
5	Excitation of the plasmon resonance in metallic nanoparticles has
6	attracted enormous interest in the past several years. This is partly
7	due to the location of the plasmon band in the near IR for particles
8	in a wide range of sizes and geometries. (Living tissue is nearly
9	transparent in the near IR, and for this reason, there is an
10	unrealized potential for metallic nanoparticles to be used in both
11	diagnostic and therapeutic settings.) One of the side effects of
12	absorption of laser radiation at these frequencies is the rapid
13	(sub-picosecond) heating of the electronic degrees of freedom in the
14	metal. This hot electron gas quickly transfers heat to the phonon
15	modes of the lattice, resulting in a rapid heating of the metal
16	particles.
17
18	Since metallic nanoparticles have a large surface area to volume
19	ratio, many of the metal atoms are at surface locations and experience
20	relatively weak bonding. This is observable in a lowering of the
21	melting temperatures and a substantial softening of the bulk modulus
22	of these particles when compared with bulk metallic samples. One of
23	the side effects of the excitation of small metallic nanoparticles at
24	the plasmon resonance is the facile creation of liquid metal
25	droplets.
26
27	Much of the experimental work on this subject has been carried out in
28	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 the electron-phonon coupling to be observed as a function of time. 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{HuM._jp020581+} Pleach {\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.
29
30
31	Since these experiments are often carried out in condensed phase
32	surroundings, the large surface area to volume ratio makes the heat
33	transfer to the surrounding solvent also a relatively rapid process.
34	In our recent simulation study of the laser excitation of gold
35	nanoparticles,\cite{VardemanC.F._jp051575r} we observed that the cooling rate for these
36	particles (10$^{11}$-10$^{12}$ K/s) is in excess of the cooling rate
37	required for glass formation in bulk metallic alloys. Given this
38	fact, it may be possible to use laser excitation to melt, alloy and
39	quench metallic nanoparticles in order to form metallic glass
40	nanobeads.
41
42	To study whether or not glass nanobead formation is feasible, we have
43	chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a
44	model system because it is an experimentally known glass former and
45	has been used previously as a theoretical model for glassy
46	dynamics.\cite{Vardeman-II:2001jn} The Hume-Rothery rules suggest that
47	alloys composed of Copper and Silver should be miscible in the solid
48	state, because their lattice constants are within 15\% of each
49	another.\cite{Kittel:1996fk} Experimentally, however Ag-Cu alloys are a
50	well-known exception to this rule and are only miscible in the liquid
51	state given equilibrium conditions. Below the eutectic temperature of
52	779 $^\circ$C and composition (60.1\% Ag, 39.9\% Cu), the
53	solid alloys of Ag and Cu will phase separate into Ag and Cu rich
54	$\alpha$ and $\beta$ phases, respectively. This behavior is due to a
55	positive heat of mixing in both the solid and liquid phases. For the
56	one-to-one composition fcc solid solution, $\Delta H$ is on the order
57	of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid solutions may be
58	formed by undercooling, and under these conditions, a
59	compositionally-disordered $\gamma$ fcc phase can be formed.
60
61	Metastable alloys composed of Ag-Cu were first reported by Duwez in
62	1960 and were created by using a ``splat quenching'' technique in
63	which a liquid droplet is propelled by a shock wave against a cooled
64	metallic target.\cite{duwez:1136} Because of the small positive
65	$\Delta H$, supersaturated crystalline solutions are typically
66	obtained rather than an amorphous phase. Higher $\Delta H$ systems,
67	such as Ag-Ni, are immiscible even in liquid states, but they tend to
68	form metastable alloys much more readily than Ag-Cu. If present, the
69	amorphous Ag-Cu phase is usually seen as the minority phase in most
70	experiments. Because of this unique crystalline-amorphous behavior,
71	the Ag-Cu system has been widely studied. Methods for creating such
72	bulk phase structures include splat quenching, vapor deposition, ion
73	beam mixing and mechanical alloying. Both structural
74	\cite{sheng:184203} and dynamic\cite{Vardeman-II:2001jn}
75	computational studies have also been performed on this system.
76
77	Although bulk Ag-Cu alloys have been studied widely, this alloy has
78	been mostly overlooked in nanoscale materials. The literature on
79	alloyed metallic nanoparticles has dealt with the Ag-Au system, which
80	has the useful property of being miscible on both solid and liquid
81	phases. Nanoparticles of another miscible system, Au-Cu, have been
82	successfully constructed using techniques such as laser
83	ablation,\cite{Malyavantham:2004cu} and the synthetic reduction of
84	metal ions in solution.\cite{Kim:2003lv} Laser induced alloying has
85	been used as a technique for creating Au-Ag alloy particles from
86	core-shell particles.\cite{Hartland:2003lr} To date, attempts at
87	creating Ag-Cu nanoparticles have used ion implantation to embed
88	nanoparticles in a glass matrix.\cite{De:1996ta,Magruder:1994rg} These
89	attempts have been largely unsuccessful in producing mixed alloy
90	nanoparticles, and instead produce phase segregated or core-shell
91	structures.
92
93	One of the more successful attempts at creating intermixed Ag-Cu
94	nanoparticles used alternate pulsed laser ablation and deposition in
95	an amorphous Al$_2$O$_3$ matrix.\cite{gonzalo:5163} Surface plasmon
96	resonance (SPR) of bimetallic core-shell structures typically show two
97	distinct resonance peaks where mixed particles show a single shifted
98	and broadened resonance.\cite{Hodak:2000rb} The SPR for pure silver
99	occurs at 400 nm and for copper at 570 nm.\cite{HengleinA._jp992950g}
100	On Al$_2$O$_3$ films, these resonances move to 424 nm and 572 nm for the pure metals. For
101	bimetallic nanoparticles with 40\% Ag an absorption peak is seen
102	between 400-550 nm. With increasing Ag content, the SPR shifts
103	towards the blue, with the peaks nearly coincident at a composition of
104	57\% Ag. Gonzalo {\it et al.} cited the existence of a single broad
105	resonance peak as evidence of a mixed alloy particle rather than a
106	phase segregated system. Unfortunately, they were unable to determine
107	whether the mixed nanoparticles were an amorphous phase or a
108	supersaturated crystalline phase. One consequence of embedding the
109	Ag-Cu nanoparticles in a glass matrix is that the SPR can be shifted
110	because of the nanoparticle-glass matrix
111	interaction.\cite{De:1996ta,Roy:2003dy}
112
113	Characterization of glassy behavior by molecular dynamics simulations
114	is typically done using dynamic measurements such as the mean squared
115	displacement, $\langle r^2(t) \rangle$. Liquids exhibit a mean squared
116	displacement that is linear in time (at long times). Glassy materials
117	deviate significantly from this linear behavior at intermediate times,
118	entering a sub-linear regime with a return to linear behavior in the
119	infinite time limit.\cite{Kob:1999fk} However, diffusion in nanoparticles
120	differs significantly from the bulk in that atoms are confined to a
121	roughly spherical volume and cannot explore any region larger than the
122	particle radius ($R$). In these confined geometries, $\langle r^2(t)
123	\rangle$ approaches a limiting value of $3R^2/40$.\cite{ShibataT._ja026764r} This limits the
124	utility of dynamical measures of glass formation when studying
125	nanoparticles.
126
127	However, glassy materials exhibit strong icosahedral ordering among
128	nearest-neghbors in contrast to crystalline or liquid structures.
129	Local icosahedral structures are the three-dimensional equivalent of
130	covering a two-dimensional plane with 5-sided tiles; they cannot be
131	used to tile space in a periodic fashion, and are therefore an
132	indicator of non-periodic packing in amorphous solids. Steinhart {\it
133	et al.} defined an orientational bond order parameter that is
134	sensitive to icosahedral ordering.\cite{Steinhardt:1983mo} This bond
135	order parameter can therefore be used to characterize glass formation
136	in liquid and solid solutions.\cite{wolde:9932}
137
138	Theoretical molecular dynamics studies have been performed on the
139	formation of amorphous single component nanoclusters of either
140	gold,\cite{Chen:2004ec,Cleveland:1997jb,Cleveland:1997gu} or
141	nickel,\cite{Gafner:2004bg,Qi:2001nn} by rapid cooling($\thicksim
142	10^{12}-10^{13}$ K/s) from a liquid state. All of these studies found
143	icosahedral ordering in the resulting structures produced by this
144	rapid cooling which can be evidence of the formation of a amorphous
145	structure.\cite{Strandburg:1992qy} The nearest neighbor information was
146	obtained from pair correlation functions, common neighbor analysis and
147	bond order parameters.\cite{Steinhardt:1983mo} It should be noted that
148	these studies used single component systems with cooling rates that
149	are only obtainable in computer simulations and particle sizes less
150	than 20\AA. Single component systems are known to form amorphous
151	states in small clusters,\cite{Breaux:rz} but do not generally form
152	amorphous structures in bulk materials. Icosahedral structures have
153	also been reported in nanoparticles, particularly multiply twinned
154	particles.\cite{Ascencio:2000qy}
155
156	Since the nanoscale Ag-Cu alloy has been largely unexplored, many
157	interesting questions remain about the formation and properties of
158	such a system. Does the large surface to volume ratio aid Ag-Cu
159	nanoparticles in rapid cooling and formation of an amorphous state?
160	Would a predisposition to isosahedral ordering in nanoparticles also
161	allow for easier formation of an amorphous state and what is the
162	preferred ordering in a amorphous nanoparticle? Nanoparticles have
163	been shown to have size dependent melting
164	transition,\cite{Buffat:1976yq} and we would expect a similar trend
165	to follow for the glass transition temperature.
166
167	In the sections below, we describe our modeling of the laser
168	excitation and subsequent cooling of the particles in silico to mimic
169	real experimental conditions. The simulation parameters have been
170	tuned to the degree possible to match experimental conditions, and we
171	discusss both the icosahedral ordering in the system, as well as the
172	clustering of icosahedral centers that we observed.
173