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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#	User	Rev	Content
1	chuckv	3226	%!TEX root = /Users/charles/Desktop/nanoglass/nanoglass.tex
2
3	chuckv	3208	\section{Introduction}
4	gezelter	3217
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	gezelter	3230	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	gezelter	3217
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	gezelter	3230	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	gezelter	3217
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	gezelter	3219	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	gezelter	3221	another.\cite{Kittel:1996fk} Experimentally, however Ag-Cu alloys are a
63	gezelter	3219	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	gezelter	3230	one-to-one composition fcc solid solution, $\Delta H_{\rm mix}$ is on the order
70	chuckv	3220	of +6~kJ/mole.\cite{Ma:2005fk} Non-equilibrium solid solutions may be
71	gezelter	3219	formed by undercooling, and under these conditions, a
72			compositionally-disordered $\gamma$ fcc phase can be formed.
73	gezelter	3217
74	gezelter	3219	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	gezelter	3230	$\Delta H_{\rm mix}$, 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	gezelter	3219	\cite{sheng:184203} and dynamic\cite{Vardeman-II:2001jn}
89			computational studies have also been performed on this system.
90	chuckv	3218
91	gezelter	3219	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	gezelter	3221	core-shell particles.\cite{Hartland:2003lr} To date, attempts at
101	gezelter	3219	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	chuckv	3218
107	gezelter	3219	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	chuckv	3222	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	gezelter	3219	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	chuckv	3222	57\% Ag. Gonzalo {\it et al.} cited the existence of a single broad
119	gezelter	3219	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	chuckv	3218
127	gezelter	3219	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	chuckv	3220	infinite time limit.\cite{Kob:1999fk} However, diffusion in nanoparticles
134	gezelter	3219	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, $\langle r^2(t)
137	chuckv	3220	\rangle$ approaches a limiting value of $3R^2/40$.\cite{ShibataT._ja026764r} This limits the
138	gezelter	3219	utility of dynamical measures of glass formation when studying
139			nanoparticles.
140	chuckv	3218
141	gezelter	3219	However, glassy materials exhibit strong icosahedral ordering among
142	gezelter	3230	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	chuckv	3218
153	gezelter	3219	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	gezelter	3230	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	gezelter	3219	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	chuckv	3218
171	gezelter	3219	Since the nanoscale Ag-Cu alloy has been largely unexplored, many
172			interesting questions remain about the formation and properties of
173	gezelter	3230	such a system. Does the large surface area to volume ratio aid Ag-Cu
174	gezelter	3219	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	gezelter	3230	transition,\cite{Buffat:1976yq} so we would expect a similar trend to
180			follow for the glass transition temperature.
181	chuckv	3218
182	gezelter	3219	In the sections below, we describe our modeling of the laser
183	gezelter	3230	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	chuckv	3218