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 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{HuM._jp020581+} 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.

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 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. 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, $\Delta H_{\rm mix}$ 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.

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 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 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. 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 area 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} so 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 {\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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#	Content
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
29	groups.\cite{HartlandG.V._jp0276092,Hodak:2000rb,Hartland:2003lr,Petrova:2007qy,Link:2000lr}
30	These experiments mostly use the technique of time-resolved optical
31	pump-probe spectroscopy where a pump laser pulse serves to excite
32	conduction band electrons in the nanoparticle and a following probe
33	laser pulse allows observation of the time evolution of the
34	electron-phonon coupling. Hu and Hartland have observed a direct
35	relation between the size of the nanoparticle and the observed cooling
36	rate using such pump-probe techniques.\cite{HuM._jp020581+} Plech
37	{\it et al.} have use pulsed x-ray scattering as a probe to directly
38	access changes to atomic structure following pump
39	excitation.\cite{plech:195423} They further determined that heat
40	transfer in nanoparticles to the surrounding solvent is goverened by
41	interfacial dynamics and not the thermal transport properties of the
42	solvent.
43
44	Since these experiments are often carried out in condensed phase
45	surroundings, the large surface area to volume ratio makes the heat
46	transfer to the surrounding solvent also a relatively rapid process.
47	In our recent simulation study of the laser excitation of gold
48	nanoparticles,\cite{VardemanC.F._jp051575r} we observed that the
49	cooling rate for these particles (10$^{11}$-10$^{12}$ K/s) is in
50	excess of the cooling rate required for glass formation in bulk
51	metallic alloys. Given this fact, it may be possible to use laser
52	excitation to melt, alloy and quench metallic nanoparticles in order
53	to form glassy nanobeads.
54
55	To study whether or not glass nanobead formation is feasible, we have
56	chosen the bimetallic alloy of Silver (60\%) and Copper (40\%) as a
57	model system because it is an experimentally known glass former and
58	has been used previously as a theoretical model for glassy
59	dynamics.\cite{Vardeman-II:2001jn} The Hume-Rothery rules suggest that
60	alloys composed of Copper and Silver should be miscible in the solid
61	state, because their lattice constants are within 15\% of each
62	another.\cite{Kittel:1996fk} Experimentally, however Ag-Cu alloys are a
63	well-known exception to this rule and are only miscible in the liquid
64	state given equilibrium conditions. Below the eutectic temperature of
65	779 $^\circ$C and composition (60.1\% Ag, 39.9\% Cu), the
66	solid alloys of Ag and Cu will phase separate into Ag and Cu rich
67	$\alpha$ and $\beta$ phases, respectively. This behavior is due to a
68	positive heat of mixing in both the solid and liquid phases. For the
69	one-to-one composition fcc solid solution, $\Delta H_{\rm mix}$ is on the order
70	of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid solutions may be
71	formed by undercooling, and under these conditions, a
72	compositionally-disordered $\gamma$ fcc phase can be formed.
73
74	Metastable alloys composed of Ag-Cu were first reported by Duwez in
75	1960 and were created by using a ``splat quenching'' technique in
76	which a liquid droplet is propelled by a shock wave against a cooled
77	metallic target.\cite{duwez:1136} Because of the small positive
78	$\Delta H_{\rm mix}$, supersaturated crystalline solutions are
79	typically obtained rather than an amorphous phase. Higher $\Delta
80	H_{\rm mix}$ systems, such as Ag-Ni, are immiscible even in liquid
81	states, but they tend to form metastable alloys much more readily than
82	Ag-Cu. If present, the amorphous Ag-Cu phase is usually seen as the
83	minority phase in most experiments. Because of this unique
84	crystalline-amorphous behavior, the Ag-Cu system has been widely
85	studied. Methods for creating such bulk phase structures include splat
86	quenching, vapor deposition, ion beam mixing and mechanical
87	alloying. Both structural
88	\cite{sheng:184203} and dynamic\cite{Vardeman-II:2001jn}
89	computational studies have also been performed on this system.
90
91	Although bulk Ag-Cu alloys have been studied widely, this alloy has
92	been mostly overlooked in nanoscale materials. The literature on
93	alloyed metallic nanoparticles has dealt with the Ag-Au system, which
94	has the useful property of being miscible on both solid and liquid
95	phases. Nanoparticles of another miscible system, Au-Cu, have been
96	successfully constructed using techniques such as laser
97	ablation,\cite{Malyavantham:2004cu} and the synthetic reduction of
98	metal ions in solution.\cite{Kim:2003lv} Laser induced alloying has
99	been used as a technique for creating Au-Ag alloy particles from
100	core-shell particles.\cite{Hartland:2003lr} To date, attempts at
101	creating Ag-Cu nanoparticles have used ion implantation to embed
102	nanoparticles in a glass matrix.\cite{De:1996ta,Magruder:1994rg} These
103	attempts have been largely unsuccessful in producing mixed alloy
104	nanoparticles, and instead produce phase segregated or core-shell
105	structures.
106
107	One of the more successful attempts at creating intermixed Ag-Cu
108	nanoparticles used alternate pulsed laser ablation and deposition in
109	an amorphous Al$_2$O$_3$ matrix.\cite{gonzalo:5163} Surface plasmon
110	resonance (SPR) of bimetallic core-shell structures typically show two
111	distinct resonance peaks where mixed particles show a single shifted
112	and broadened resonance.\cite{Hodak:2000rb} The SPR for pure silver
113	occurs at 400 nm and for copper at 570 nm.\cite{HengleinA._jp992950g}
114	On Al$_2$O$_3$ films, these resonances move to 424 nm and 572 nm for the pure metals. For
115	bimetallic nanoparticles with 40\% Ag an absorption peak is seen
116	between 400-550 nm. With increasing Ag content, the SPR shifts
117	towards the blue, with the peaks nearly coincident at a composition of
118	57\% Ag. Gonzalo {\it et al.} cited the existence of a single broad
119	resonance peak as evidence of a mixed alloy particle rather than a
120	phase segregated system. Unfortunately, they were unable to determine
121	whether the mixed nanoparticles were an amorphous phase or a
122	supersaturated crystalline phase. One consequence of embedding the
123	Ag-Cu nanoparticles in a glass matrix is that the SPR can be shifted
124	because of the nanoparticle-glass matrix
125	interaction.\cite{De:1996ta,Roy:2003dy}
126
127	Characterization of glassy behavior by molecular dynamics simulations
128	is typically done using dynamic measurements such as the mean squared
129	displacement, $\langle r^2(t) \rangle$. Liquids exhibit a mean squared
130	displacement that is linear in time (at long times). Glassy materials
131	deviate significantly from this linear behavior at intermediate times,
132	entering a sub-linear regime with a return to linear behavior in the
133	infinite time limit.\cite{Kob:1999fk} However, diffusion in nanoparticles
134	differs significantly from the bulk in that atoms are confined to a
135	roughly spherical volume and cannot explore any region larger than the
136	particle radius ($R$). In these confined geometries, $\langle r^2(t)
137	\rangle$ approaches a limiting value of $3R^2/40$.\cite{ShibataT._ja026764r} This limits the
138	utility of dynamical measures of glass formation when studying
139	nanoparticles.
140
141	However, glassy materials exhibit strong icosahedral ordering among
142	nearest-neghbors (in contrast with crystalline and liquid-like
143	configurations). Local icosahedral structures are the
144	three-dimensional equivalent of covering a two-dimensional plane with
145	5-sided tiles; they cannot be used to tile space in a periodic
146	fashion, and are therefore an indicator of non-periodic packing in
147	amorphous solids. Steinhart {\it et al.} defined an orientational
148	bond order parameter that is sensitive to icosahedral
149	ordering.\cite{Steinhardt:1983mo} This bond order parameter can
150	therefore be used to characterize glass formation in liquid and solid
151	solutions.\cite{wolde:9932}
152
153	Theoretical molecular dynamics studies have been performed on the
154	formation of amorphous single component nanoclusters of either
155	gold,\cite{Chen:2004ec,Cleveland:1997jb,Cleveland:1997gu} or
156	nickel,\cite{Gafner:2004bg,Qi:2001nn} by rapid cooling($\thicksim
157	10^{12}-10^{13}$ K/s) from a liquid state. All of these studies found
158	icosahedral ordering in the resulting structures produced by this
159	rapid cooling which can be evidence of the formation of an amorphous
160	structure.\cite{Strandburg:1992qy} The nearest neighbor information
161	was obtained from pair correlation functions, common neighbor analysis
162	and bond order parameters.\cite{Steinhardt:1983mo} It should be noted
163	that these studies used single component systems with cooling rates
164	that are only obtainable in computer simulations and particle sizes
165	less than 20\AA. Single component systems are known to form amorphous
166	states in small clusters,\cite{Breaux:rz} but do not generally form
167	amorphous structures in bulk materials. Icosahedral structures have
168	also been reported in nanoparticles, particularly multiply twinned
169	particles.\cite{Ascencio:2000qy}
170
171	Since the nanoscale Ag-Cu alloy has been largely unexplored, many
172	interesting questions remain about the formation and properties of
173	such a system. Does the large surface area to volume ratio aid Ag-Cu
174	nanoparticles in rapid cooling and formation of an amorphous state?
175	Would a predisposition to isosahedral ordering in nanoparticles also
176	allow for easier formation of an amorphous state and what is the
177	preferred ordering in a amorphous nanoparticle? Nanoparticles have
178	been shown to have size dependent melting
179	transition,\cite{Buffat:1976yq} so we would expect a similar trend to
180	follow for the glass transition temperature.
181
182	In the sections below, we describe our modeling of the laser
183	excitation and subsequent cooling of the particles {\it in silico} to
184	mimic real experimental conditions. The simulation parameters have
185	been tuned to the degree possible to match experimental conditions,
186	and we discusss both the icosahedral ordering in the system, as well
187	as the clustering of icosahedral centers that we observed.
188