trunk/nanoglass/introduction.tex

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