Clusters: A New State of Matter
Spring, 1991
By Lynn Yarris, LCYarris@LBL.gov
Clusters can be formed from any element on the periodic chart. They
can be composed of a single type of atom -- an "elemental cluster" --
or they can be composed of two or more different types of atoms or
molecules. Depending on their composition, they can be metallic or
non-metallic. There are electrically neutral clusters, and there are
electrically-charged "ionic" clusters. What all clusters have in
common, however, is their in-between size: they are too large to be
thought of as a molecule but too small to be classified as a liquid or
a solid. Consequently, clusters frequently exhibit physical and
chemical properties not seen in bulk phase materials -- properties that
scientists hope to exploit in a broad number of areas.
For example, unlike in a liquid or a solid, nearly all of the atoms in
a cluster are on or near its surface. Because of this, a cluster's
reactivity can often be enhanced or diminished with the loss or
addition of a single atom. As a result, clusters can be used as highly
effective catalysts. Other clusters have optical properties that could
allow their use in a new generation of micro-miniature, high-capacity
data storage disks for computers. There is also the possibility that
certain types of clusters can be assembled into exotic new bulk
materials, such as stronger and more flexible ceramics.
For the potential of clusters as a source of new materials to be
realized, however, a great deal of basic research will have to be
done. Scientists need to know more about the geometric and electronic
structures of clusters -- how their constituent atoms and electrons are
arranged -- and the properties that result from these structures.
Especially important is understanding how the different properties of a
cluster depend upon its size.
Explains Daniel Chemla, head of LBL's Materials Science Division (MSD),
and an expert on quantum-size effects in semiconductors, "The smaller
the cluster, the higher its surface-to-volume ratio and the more
important its surface becomes. All of the physical properties of a
cluster -- electronic, optical, photochemical, thermodynamic, etc., --
eventually are become size-dependent."
To study the structures and properties of the smallest clusters --
elemental cluster systems between 3 and 11 atoms in size -- Daniel
Neumark, a chemist with LBL's Chemical Sciences Division (CSD), and a
professor with the University of California Berkeley (UCB), is using a
technique called "negative ion photoelectron spectroscopy." With this
technique, Neumark and his colleagues are able to determine the
vibrational frequencies of the chemical bonds in a size-selected
elemental cluster. This reveals the strengths and angles of those
chemical bonds.
"In the past, knowing the size of the clusters with which you were
working was a real problem," says Neumark. "We can now eliminate this
ambiguity."
Neumark and his colleagues create cluster anions by focusing a laser on
a target made from whatever element they wish to study. Atoms vaporized
off the surface of the target are entrained in a jet of inert gas which
in turn is expanded through a supersonic nozzle into a vacuum for
cooling. As the gas cools, a variety of neutral and ionic clusters are
formed. Negative cluster ions are extracted and separated according to
size through the use of mass spectrometry.
Vibrational frequencies of the selected clusters are measured by
shining a fixed-frequency pulsed laser on them to detach electrons.
The energies of a small fraction of these photodetached electrons are
determined by recording their time-of-flight through a one meter long
flight tube with a detector at the end. This provides a spectra that
yields information on the electronic states and the vibrational
frequencies of the neutral clusters formed when the photoelectrons were
detached.
"Our spectra are obtained at considerably higher resolution than has
been previously reported, which has enabled us to observe vibrational
features," says Neumark. "Since some of our experimental findings have
been consistent with theoretical predictions, we feel we are getting an
accurate picture of the structures we are studying."
So far, Neumark and his colleagues have studied small silicon and
carbon clusters. The group plans to next study these same clusters
using a technique called "threshold photodetachment spectroscopy," in
which a tunable laser is used for the detaching and collecting of only
ground state electrons.
"This experiment, which we have already applied to silicon and carbon,
will give us even higher resolution and should provide us with much
more information on the vibrational frequencies and low-lying
electronic states of small silicon and carbon clusters," Neumark says.
While coupling laser vaporization with a supersonic expansion to make
clusters provides the kind of size-specific quality control needed for
structural studies, it does not yield the high quantities of clusters
that are important for exploring physical properties.
"The range of cluster phenomena that can be studied now is limited by
the availability of samples. We need to make clusters in large enough
quantities that they can be studied under a variety of different
conditions," says Paul Alivisatos, a chemist with LBL's Materials
Science Division (MSD) and UCB professor. He and his group are using
chemical methods to produce powders that may contain millions of
individual clusters.
The technique they use starts with "nucleation" or the formation of
crystal nuclei in solution that will react to form a desired type of
cluster. As the clusters formed in the reaction come together, they
combine and grow in size. This "growth" is continued until the
researchers have the size they want, at which point growth is
chemically "terminated," and the clusters are precipitated out of
solution. The clusters produced by Alivisatos and his group with this
technique have ranged in size from 100 to 10,000 or more atoms.
The selection for a specific size of cluster using chemical production
methods, however, is rough. Says Alivisatos, "We typically see a
variation of about 5-percent in the size of the clusters we produce,
which is not as good as it could be. However, because we make so much
material we can do more experiments with our samples."
Alivisatos and his group first used chemical techniques to synthesize
clusters of the semiconductor cadmium sulfide in the form of
nanocrystals (crystalline particles that are a billionth of a meter, or
a few angstroms, in diameter). These nanocrystals were then deposited
on a metal surface and imaged for study at LBL's National Center for
Electron Microscopy (NCEM) by UCB chemist Avery Goldstein. One of
these studies demonstrated the effect of size on the temperature at
which a material will melt. In the bulk-phase, cadmium sulfide has a
melting point of 1,750 kelvin (1,477 degrees Celsius), but the cadmium
sulfide clusters analyzed at NCEM showed a melting point less than half
that -- 575 kelvin.
"The observed depression in the melting point of these semiconductor
clusters is similar to effects observed in metals and molecular
crystals, indicating that the phenomenon of reduced melting points in
small systems is a general one regardless of the type of material,"
says Alivisatos. "The observation of melting point depression in these
clusters also has far reaching implications for the preparation of
highly crystalline clusters of cadmium sulfide, as well for the use of
these nanocrystal clusters as precursors to thin films."
Again using chemical production methods, Alivisatos and his group
became the first to synthesize large quantities of clusters of the
semiconductor gallium arsenide. In the field of semiconductor
research, gallium arsenide has moved to center stage because of its
unique electronic and optical properties. One big dream is to use
clusters of gallium arsenide to make "quantum dots" -- nanometer-sized
crystals with potential applications in photonics and electronics.
At Berkeley, such crystals were made by reacting gallium trichloride
with trimethylsilyl arsine in the solvent quinoline at a temperature of
240[[ring]]C for three days. When the solvent was removed, they had a
red powder that was then analyzed at NCEM to reveal football-shaped
clusters of gallium arsenide with a major axis of 45 angstroms and a
minor axis of 35 angstroms.
Now that scientists know how to make both large and small isolated
clusters, the next step, Alivisatos says will be to assemble these
noninteracting clusters into organized arrays.
"We think we can make isolated clusters of sufficient size to study
their properties, but if we are ever going to put these materials into
commercial applications, we will need to be able to make crystals of
clusters," he says. "The trick will be to create a cluster core of
maybe 100 atoms, stabilize it so it can't react, and then crystalize
it."
Making crystals out of clusters is not likely to happen soon,
Alivisatos says. More experimental work on large isolated cluster
systems is needed, as are theoretical models that can help the
experimentalists interpret their findings. Existing models are good
for no more than three atoms.
"Theory has been way behind the experiments for large cluster systems
in part because some scientists were treating these clusters as giant
molecules, while others were treating them as extended solids," says
MSD physicist and UCB professor Marvin Cohen, a theorist who has
developed a number of models for predicting new materials and
explaining their structure and properties.
Working with UCB physicist Walter Knight and others, Cohen brought
credibility to what he calls a "jellium model" for large clusters of
metal atoms in which the clusters exhibit a "shell structure" like that
of atomic nuclei.
Within the nucleus of an atom, each proton or neutron occupies a
discrete energy level called a "shell" (or a subshell) similar to the
positioning of electrons outside the nucleus. The most stable and
abundant nuclei are those with a certain number of protons and neutrons
in their outermost shells, which have been dubbed "magic numbers."
Cohen and his colleagues have shown that metal clusters have magic
numbers too, wherein the most stable and abundant clusters are those
that contain certain numbers of atoms. This explains why certain sizes
dominate the observed spectra of sodium clusters.
"Our model treats the clusters as essentially a jelly with no structure
at all," says Cohen. "Magic numbers give these systems stability
because of shells."
In the jellium model, a metal cluster becomes a single giant atom with
a positively charged core surrounded by essentially free-roaming
electrons that respond quantum mechanically to the positive potential.
From this premise, the model has correctly predicted the observed
electronic properties of simple metal clusters, such as sodium and
copper, as a function of the number of free electrons.
The jellium model has also been used to demonstrate that clusters, like
atoms, can be classified as metallic or nonmetallic on the basis of
their ionization potential -- the minimal amount of energy required to
remove an electron. In the case of clusters, ionization potentials are
measured as a function of the number of atoms in the cluster. Knowing
the ionization potential of clusters is crucial to a lot of research
since neutral clusters must be ionized to make their detection
possible.
In addition to the jellium model, Cohen has also helped extend to
clusters a model for calculating the energies of excited state
electrons that was originally applied to semiconductors and
insulators. More precise theoretical calculations of excited states in
clusters should make it easier for experimentalists to investigate
their optical and electronic properties, including ionization
potentials and polarizabilities. Working with LBL physicist Steven
Louie, one of the developers of the original model, Cohen has used his
adaptation to calculate the optical properties of sodium and potassium
clusters. The model's predictions were close to experimental
findings.
The discovery of shell structure in clusters opens a number of research
doors, Cohen says, including the exploration of cluster magnetic
properties. He also feels that the similarities between cluster energy
shells and those found in atomic nuclei can benefit the research of
nuclear scientists.
For chemists, an area considered by many to be a holy grail is the
study of matter as it evolves from the gas to the liquid state. New
knowledge about this transition is expected to come from a better
understanding of the formation and structure of ionic clusters.
Ionic clusters consist of a single ion surrounded by one or more
neutral molecules. They are created when a gas is cooled. Molecules in
the gaseous state are widely separated and move about in continual
motion. So widely separated in space are these molecules that they
exert no force of attraction upon one another, and although they
frequently collide, their kinetic energy is so high they will not stick
together. As the temperature in the gas drops, however, molecular
motion slows and the molecules begin to gather. Eventually, the motion
slows sufficiently for intermolecular forces of attraction to bind the
molecules together into clusters that number from a few to a few
hundred individual molecules in size. If the number of neutral
molecules surrounding the ion in each cluster becomes sufficiently
large, an assemblage of clusters will resemble a conventional bulk
material--either a liquid or a solid.
Although the chemical properties of ionic clusters have been
extensively evaluated, measurements of their structures are still rare
because the infrared spectroscopy techniques routinely used to study
molecules have not been applicable. However, a new technique for
probing ionic cluster structures has been developed and used
successfully by a team of LBL and UCB scientists led by Nobel laureate
Yuan T. Lee of the Chemical Sciences Division.
Usually, when chemists want to know about molecular structures, they
use infrared spectroscopy. When a molecule absorbs an infrared photon,
it will begin vibrating and rotating at characteristic frequencies.
Measuring these "resonant vibrational-rotational frequencies"
identifies the molecule and characterizes its chemical bonds.
"But using infrared spectroscopy to study ionic clusters is a special
challenge," says Lee. "The difficulty is caused largely by the very
low ion densities one can obtain. To overcome this limitation, we have
used consequence spectroscopy, where the consequence of absorbing an
infrared photon is an observable event."
This "consequence" spectroscopy technique involves an arrangement of
tandem mass spectrometers, a radio-frequency ion trap, and a tunable
infrared laser. Cluster ions are produced by passing an electric
discharge through a gas mixture and expanding the ionized gas into a
vacuum to cool it. Clusters form in the expansion as neutral molecules
gather around ionic species. A mass spectrometer is used to separate
the clusters according to size. Ionic clusters that have been chosen
for study are then directed into the ion trap where they can be held
for exposure to infrared laser light that selectively excites specific
vibrational frequencies of their chemical bonds. When the
vibrationally excited clusters are further exposed to laser radiation,
they will continue to absorb energy until eventually they break up.
The resulting fragments can then be detected and counted with the aid
of a second mass spectrometer.
Says John Price, a chemist who worked with Lee on this project, "The
fragmentation is a consequence of the ionic clusters absorbing many
photons from the infrared laser. What we see is a product signal that
depends on the frequency of the infrared light. Therefore, by tuning
the laser and counting the fragments produced, we can obtain an
infrared absorption spectrum for the cluster."
Adds Lee, "The combination of a tandem mass spectrometer system and a
radio-frequency ion trap is ideal for the detection of dissociation
products because there is little or no background at the fragment ion
mass, and every fragment ion can be detected with nearly perfect
efficiency."
Lee, Price, and Mark Crofton recently used this new technique to do a
spectroscopic study of ammoniated ammonium ion clusters (an ammonium
ion surrounded by one to ten molecules of ammonia). In their study,
the research team recorded the first observation of internal rotation
within an ionic cluster -- the rotation of the ammonia molecules around
their bonds to the ion core. They also demonstrated that the
correlation of infrared spectral features with cluster size can provide
information about a cluster's geometrical structure and how its
physical properties change as liquids and solids form.
Since the spectra of ionic clusters in a gas phase are much easier to
interpret than the very broad and complicated spectra of molecules in a
liquid phase, Lee's group believes their new technique should also
provide a better understanding of molecular interactions that take
place in solutions.
Says Price, "It is much easier to understand the complicated
interactions that are involved in a liquid if we can start with an
isolated molecule and build up the complicated environment one molecule
at a time. Our technique makes this possible."
For his contribution to the ammoniated ammonium ion research, Price
received a Proctor Gamble Award for Graduate Research from the American
Chemical Society.
Scientists have known about the existence of clusters for many years,
but it has only been within the past ten years that the research tools,
particularly lasers, needed to study this strange new form of matter
have become available. The result has been a burgeoning of cluster
research from which has come a pivotal shift in scientific approach
that could prove to have profound ramifications even beyond the
immediate areas of catalysis, microelectronics, and advanced materials
fabrication.
Says Chemla, "In cluster research we are seeing a convergence of
scientific disciplines where people of different fields of expertise
are having to collaborate in order to get things done. It is a
convergence that is going to change the way we think of materials
sciences."
A femtosecond is a millionth of a billionth, or one quadrillionth, of a
second. To appreciate the brevity of the femtosecond time-scale,
consider this: there are as many femtoseconds in one second, as there
are seconds in 30 million years. Femtosecond lasers can produce
strobe-like pulses of light in bursts as short as six femtoseconds.
The femtosecond laser has made it possible for scientists to study the
movements of electrons within clusters, a critical factor in
determining electronic properties and, ultimately, how useful clusters
can be as semiconductors. Today's semiconductors are made from bulk
solids which are three-dimensional and provide electrons with a lot
room for movement. Because of their tiny size, clusters can present
the designers of future microelectronic devices with two-, one-, and
even zero-dimensional systems in which electron movement is much more
confined.
"Typically, in a solid an electron moves one angstrom in one
femtosecond, so if you want to see electrons move a few angstroms you
need a femtosecond laser," says physicist Daniel Chemla, who heads
LBL's Materials Science Division and is recognized as one of the
world's foremost authorities on the optical and electronic properties
of materials. "Femtoseconds are the natural time-scale for studying
electronic dynamics in nanometer-size solids such as clusters."
Producing femtosecond pulses of light requires that a broad
spectrum of white light be synchronized so that all of the
different wavelengths in the spectrum are in phase -- meaning they all
move in step. Normally, white light is "chaotic" because it is a
composition of different color bands of light, and each band has its
own wavelength and frequency.
In the femtosecond laser pioneered by Shank, this process starts with a
colliding pulse mode-locked (CPM) dye laser that is capable of
synchronizing the phases of several different modes or colors of light
at once. Essentially, the CPM is a cavity filled with an assortment of
dyes. When pumped by a low-power (four watts) argon laser, it
generates 50 femtosecond pulses of laser light that are then sent
through a second dye-filled cavity where they are amplified by six
orders of magnitude.
Each pulse of light is compressed through a length of silica fiber to
broaden its spectrum. Energy is dispersed from the fiber to the
different wavelengths of light in the pulse, causing each wavelength to
emerge from the fiber at a slightly different time. Two diffraction
gratings are positioned in such a way as to catch and bring these
different wavelengths back into phase. A series of prisms further
compresses the pulses and improves the synchronization of their
constituent light. The emerging six femtosecond pulse lengths of light
have a bandwidth of about 150 nanometers. This bandwidth can be
shifted so that it spans select sections of the spectrum, for example,
from green light to red (550 to 700 nanometers), or from red light to
infrared (700 to 850 nanometers).
The laser used by Chemla produces femtosecond pulses of infrared
radiation. "In general, I am interested in quantum size effects on
semiconductors, what happens in the transition from the
three-dimensional universe that we know to systems of reduced
dimensionality. Infrared light makes it easier to observe some of
these special properties in materials," he says.
Infrared light is also ideal for the spectroscopic study of molecular
vibrational motions -- how the bonds of a molecule vibrate when excited
by infrared photons. Such vibrations can serve as a "fingerprint" to
identify a known molecule, or reveal the geometry and bond strength of
one that has not been characterized before. To date, however, little
is known about the infrared spectroscopic characteristics of most
clusters because of a dearth in sources of infrared light that are
"tunable" -- meaning they can provide specific wavelengths of light
from within a range of selections.
In answer to this shortage, LBL and the Sandia National Laboratories
have proposed, under the terms of the "Combustion Dynamics Initiative,"
the construction of an infrared free electron laser (IRFEL) capable of
generating intense, coherent radiation that could be tuned across
infrared wavelengths ranging between 3 and 50 micrometers. This light
would be emitted in pulses that could be as short as 10 picoseconds --
a picosecond being one trillionth of a second -- or as long as 100
microseconds.
Plans call for the IRFEL to be located at LBL in a proposed Chemical
Dynamics Research Laboratory, which would be available for use by
qualified researchers from across the nation. The facility would be
built adjacent to the Advanced Light Source (ALS), a synchrotron-based
source of laserlike x-rays and ultraviolet light (roughly one to 100
nanometers in wavelengths) which is already under construction. Beams
from the two machines could be synchronized, which, together with
conventional tunable lasers, a molecular beam machine, and
state-of-the-art spectroscopic equipment, would give scientists
unmatched capabilities for studying a breathtakingly wide range of
phenomena, including clusters.
Says Daniel Neumark, a chemist with LBL's Chemical Sciences Division,
"With the ALS, we could detach electrons from neutral clusters to
ionize them, then use the IRFEL to probe them through vibrational
spectroscopy."
The IRFEL will extract its light from a beam of "free" electrons --
electrons not bound to any atom or molecule -- generated in a 50
million electron volt linear accelerator and sent at nearly the speed
of light through an undulator -- an array of dipole magnets with
alternating north and south poles. Passage through this alternating
magnetic field forces the electrons to oscillate sideways, causing them
to radiate at infrared frequencies. Coherent light is then obtained in
the same manner as a conventional laser, by bouncing the emitted
radiation back and forth between a total and a partially reflecting
mirror. The light is tuned to a specific wavelength either by changing
the spacing between the undulator's magnetic poles, or by changing the
speed or energy of the electrons passing through.
In addition to spectroscopy studies of clusters, the proposed IRFEL
could also be used to study cluster ionization potentials and bond
energies, and cluster reactivity. All of these factors are crucial if
the bright promise of clusters as a new and better class of advanced
materials is to be realized.
We all learned in high school science classes about three states of
matter: solid, liquid, and gaseous. Liquids were described as the
bridge between gases and solids, possessing a definite volume but no
definite shape, compared to gases which have neither, and solids which
have both. Those who continued on in science learned about a fourth
and -- from a universal perspective -- more common form of matter
called a plasma, which is an ionized gas. In recent times, scientists
have added to this list yet another form of matter -- aggregates of
atoms packed into spherically shaped objects called "clusters."
Numbering as few as three or as many as 20,000 individual atoms in
size, these tiny bits of matter serve as a bridge between gases and
bulk phase materials (liquids and solids), and if you visit the
chemistry, physics, or materials sciences departments of any major
research institution today, you are almost certain to find someone who
is working with them.
Sidebar: Casting
Light on Electrons