Clusters: A New State of Matter

Spring, 1991

By Lynn Yarris,

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.

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."

Sidebar: Casting Light on Electrons

The explosion of interest in cluster research was triggered in part by the great leap forward in laser technology that has taken place during the past ten years. One of the biggest advances was the invention in 1982 of the femtosecond laser, which was led by Charles V. Shank, then an electronics engineer at AT&T Bell Laboratories, now the director of LBL.

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.