The demonstration that individual molecules can be moved and precisely positioned on a surface by means of a scanning tunneling microscope (STM), without lowering the temperature to near absolute zero, represents a key step on the road to creating new atomic and molecular structures .
In Brief:
A team of scientists
at the IBM Almaden Research Center has pioneered the use of supercomputers to simulate fundamental studies on the behavior of materials, such as rapid brittle fracture and the collapse of a type of membrane. The work has already disproved current theories about that behavior, and has pointed the way to new hypotheses.
"If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis: that all things are made of atoms, little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see there's an enormous amount of information about the world, if just a little imagination and thinking are applied."
- Richard Feynman
A materials scientist in Texas places a thin wafer of apparently pure Plexiglas into a device that pulls it in opposite directions until a fracture
develops at a notch and the two halves split apart. Theory predicts that, if the material is homogeneous and the force is applied evenly, the fracture should move in a straight line up the length of the material at the speed of sound on a surface. Yet measurements show that the actual fracture is ragged and moves at about half that speed.
What caused this divergence between theory and experiment? Perhaps there were microscopic impurities in the material. Maybe the experimental setup was faulty. Or perhaps the theory was simply incorrect. Until the advent of computer simulation and visualization, it was not possible to perform an absolutely clean experiment of this type. But Farid Abraham - physicist at the IBM Almaden Research Center and expert in computational science - has pioneered methods for conducting such experiments on the computer, and he's coming up with some surprising results.
Abraham opens many of his lectures by quoting Richard Feynman, the late Nobel Prize-winning theoretical physicist, on the quintessential importance of the atomic view of nature, with particles in perpetual motion, attracting and repelling each other. "I like to fall back on Feynman's statement when people ask me why I study such simple atomic systems," says Abraham. "What he's telling us is that we can think of much of what goes on in our real world as an ensemble of little balls. These little balls bounce around, hitting and repelling each other, and sometimes sticking because of short-range local attractions. Depending on the environment these little balls are in, we can observe all sorts of states of matter and the phenomena associated with them. I've essentially used this theme throughout my 25-year career doing computer simulation."
Mirroring nature in a computer
Abraham started his journey in 1972 by trying to understand the central problem in "nucleation theory." When any vapor condenses into a liquid, such as a cloud forming raindrops, the process starts when a small number of molecules collide, stick to one another and act as a seed for a larger droplet.
"These embryonic droplets are made up of a few tens of water molecules, much too small to observe in a laboratory," says Abraham. At the time, physicists were using classical thermodynamics and the macroscopic properties of these droplets to explain how they might evolve. Abraham realized, however, that to really understand what was going on required knowledge of their microscopic properties - the behavior of very small clusters of molecules.
"As a theorist, I was at an impasse. I needed experimental information that could not be measured in the laboratory. The solution was to resort to a computer to simulate the behavior of the molecules in a droplet," recalls Abraham, who at the time worked at the IBM Scientific Center in Palo Alto, California.
"That presented a problem. I didn't know anything about computation, so the computer was not a familiar laboratory to me," he says. Indeed, in 1972 the computer was a "familiar laboratory" to hardly anyone. Nevertheless, he went ahead with simulations of the microdroplets, and produced the first simulations of inhomogeneous condensed-phase systems - such as a liquid surface - on a computer. Since then, Abraham has simulated his "ensemble of little balls" on increasingly powerful computers to study nucleation, melting, other phase transitions and, more recently, fracture dynamics and the states of tethered membranes.
"Although I've used very idealized systems, the collective behavior of the simulated atoms is very rich, and the phenomena are generic to a broad class of materials," explains Abraham.
It's a nonlinear world
Ever since the invention of calculus, physicists have used linear approximations to describe the world. In a linear approximation, if you add two things together, their sum total is an adequate description of their combined behavior, which simplifies the mathematics.
Unfortunately, nature is dominated by nonlinear events; ones in which a small cause can have a large effect. The brilliant mathematician and computer pioneer John von Neumann argued that, because nature is nonlinear, powerful calculating machines would be needed to track the mathematics in some approximate way. "He was saying that nature's laws can be modeled as algorithms, or rules, that can be simulated on a computer," explains Abraham. "If we take the simple algorithm that Feynman postulated - of the attraction and repulsion of little balls - and sum up the collective behavior of millions of balls, we can then go ahead and really study the nonlinear behavior of fracture, condensation and other complex phenomena."
The trouble is that it takes enormous computing power to model the behavior of millions of little balls. In 1985, using the most powerful supercomputers then available, along with some creative programming techniques, Abraham was able to model systems of about 200,000 atoms. That capability allowed him to model the formation of a film of krypton atoms on graphite over a period of a few billionths of a second.
But a two-dimensional array of 200,000 atoms has only about 450 atoms on a side. That's not quite large enough to model fracture dynamics. In such a small system, the elastic shock waves produced by the advancing fracture reflect off the wafer's edges and return to the fracture point before it can get very far. This, in Abraham's words, "dirties up the system."
"However," points out Abraham, "greater size demands more atoms. More atoms demand more computation, not only because of the increase in size, but because it takes longer for the crack to traverse the system."
A third mode of science
The solution to this dilemma proved to be parallel computation. Using parallel computers, Abraham and his colleagues, William Rudge, Rick Rafey and Dominique Brodbeck (a visualization expert), have modeled the dynamics of brittle fracture in systems of tens of millions of atoms. Their experiments are revealing some surprises. When they pull apart their simulated wafer, the crack starts out straight, but then it starts zigzagging. Because of this zigzag motion, the fracture advances at considerably less than the speed predicted by theory.
"Because we're simulating an absolutely pure system, we know for sure that the instability and the speed limitations have nothing to do with impurities in the material or difficulties in the experimental setup; they're inherent properties of the dynamics itself," says Abraham.
"In a certain sense," he says, "one can view the simulation methodology as giving experimental information about an idealized world." Some view this approach as a mixture of theory and experiment and have labeled it a "third mode of science."
"By computationally solving the theoretical models in full detail, a wealth of information about a physical phenomenon is produced that may be viewed as experimental data," he says. "In a real sense I become an experimentalist. Like any experimentalist, I have to ask the right questions, and I have to measure the right things."
One of the measurements he's made is of the patterns of stress in the wafer as it begins to pull apart. Significant departures from linear elasticity theory are seen when the crack becomes unstable. At about one-half the limiting velocity of the crack, when the direction of the crack tip begins to change from a straight line to a zigzag motion, dislocations in the surrounding materials occur that appear to be emitted from the crack itself. Abraham emphasizes that the next important step is to incorporate these observations into a unified theory - one that can predict what happens in a broad range of systems and under various conditions - for brittle fracture.
Tethered membranes
While Abraham found a surprising instability in his simulations of fracture dynamics, he found a surprising stability in his simulations of tethered membranes. Theorists know that a long, one-dimen-
sional polymer chain in a solvent will collapse into a loose ball. They predicted that a two-dimensional tethered membrane would respond similarly, much like a crushed piece of paper containing a number of voids.
Abraham's simulations proved the theorists wrong. He modeled a tethered membrane as a network of particles, or balls, each tied to its six nearest neighbors with flexible strings. At first he assumed no attractive interactions between the balls; the only restriction he imposed was that the balls couldn't pass through each other. To his surprise the membrane didn't collapse at all. It rolled, wrinkled and undulated, but it didn't collapse, revealing an unusual degree of structural rigidity.
Then Abraham started tweaking the system. First, he added an attractive interaction between the balls. Not so surprisingly, the membrane immediately collapsed into a tight clump. Yet one feature he had not anticipated was that the clump was too tight - the balls packed together as densely as in a liquid or a solid, having virtually none of the predicted voids. "At first the theorists didn't believe it," says Abraham. "These atoms are tied together in a very complex way in this net, and it's hard to believe they would collapse with such a tight packing density."
Then he raised the effective "temperature" in his experimental system. At a high enough temperature, even a membrane with attractive interactions would maintain its flat shape. But, as Abraham slowly lowered the system temperature, he recalls, "the most amazing thing happened. All of a sudden, at a particular temperature, the membrane folded almost perfectly in half. Then I lowered the temperature once more. It folded in half again. Then I lowered it again. It folded a third time." These "observations" have now been explained theoretically, but they were first seen in computer simulations.
Simulating real materials
Despite his successes, Abraham points out that "we still have real limitations in doing simulations on the computer. We're forced to go to idealized systems. In the case of fracture dynamics, one idealization is two dimensions. But I have started to add some thickness to these things. I'm starting to study slabs on the order of 20 atoms thick."
Another idealization is his use of generic atoms in his simulations. "In order to convince the real practitioners of fracture dynamics, I'm going to have to simulate a real material," says Abraham.
First on his agenda is a simulation of a silicon crystal, which will require a more sophisticated description of how the individual atoms interact. The behavior of atoms in the idealized system is completely dependent on simple interactions between an atom and its nearest neighbors. In a silicon crystal, on the other hand, the atoms are connected by covalent bonds, they are situated in a particular crystallographic orientation, and their behavior depends on a much more complex atomistic environment.
In addition, Abraham and his colleagues, who up to this point have used classical Newtonian mechanics, are about to start bringing in quantum-mechanical calculations. "We're interested in finding out what the redistribution of electrons in bond breaking might do to the fracture mechanism," he says.
Abraham has named this project MAAD, an acronym for Macro-Atomistic-Ab initio-Dynamics. The goal of the project is to show how the continuum description couples to the empirical atomistic description and how that, in turn, couples to the quantum description - all in a seamless way. He calls this the "Holy Grail of Computational Science," and he is pursuing it with the other members of the MAAD coalition, which consists of researchers from IBM, Harvard, Brown, Stanford and the Naval Research Laboratory.
This approach, Abraham concedes, represents a departure from the universality of Feynman's simplified atomistic picture of matter; the physics at different-size scales is substantially different. Yet, Abraham is confident that a unified description is possible, and, indeed, he says, "we have already coupled the continuum description to the atomistic." By suitably representing the atoms and forces, the MAAD coalition scientists have been able to simulate a sound wave propagating through a block of matter while the physics changes from a continuum description to an atomistic one. "The fact that the wave is not reflected at the point where the description changes," says Abraham, "means that we have correctly modeled the connection between the two descriptive regimes. Had the wave 'seen' a discontinuity, it would have been partly or entirely reflected." Although the group is not yet claiming that they are in possession of the Grail, the seam is fast disappearing.
"I am very fortunate," says Abraham. "I have so many very good people working with me at IBM who know the computers, know how to do sophisticated programming, know how to maintain systems, know about visualization. Without their help, I couldn't have done any of this at the level I'm doing it now."
Robert Finn is a freelance science writer based in Long Beach,
California.
