Modeling material defects
Theory and experiment improve our understanding of materials
New technology promises to improve the efficiency of nuclear reactors and to reduce waste, but it also requires careful consideration of how higher temperatures and intense radiation fields affect the materials with which reactors are built.
"Metallurgy is a very old subject, so you might think that by this point we would understand everything about it. However, that's not the case," says Malcolm Stocks, director of ORNL's Center for Defect Physics. The CDP is conducting groundbreaking research into the structure and performance of materials used in nuclear reactors and other applications where radiation damage is a concern.
Dhiraj Catoor uses a high-resolution x-ray diffractometer to study defect interactions in structural materials. Photo: Jason Richards
Radiation damage begins when a material, steel for instance, is struck by a high-energy neutron. The core of a nuclear reactor is full of very energetic neutrons. When one of these strikes an atom in the reactor vessel, it knocks the atom out of its normal position in the lattice-like atomic structure that is characteristic of the steel alloys used in high-radiation applications.
"That atom hits another one, which hits another, and so on," Stocks says. "Pretty soon you have thousands of them knocked out of place. Most of the time, this is a very transient effect, and these atoms very quickly go back to their original positions. The few that don't are the defects that will remain and will eventually interact with other defects to form larger flaws that cause the material to become brittle, to crack, or to swell.
"There are features of the radiation damage process which no one has ever measured," Stocks explains. "They happen extremely quickly—inside chunks of material—so it's very difficult to see them."
Because no measurements have ever been made of the process of defect formation, researchers' understanding of the phenomenon is based on simulations rooted in classical molecular dynamics, which describes the basic physical interactions among atoms. The CDP proposes to achieve a more thorough accounting of the process by making the first-ever measurements of several aspects of defect formation and then creating a much more accurate and comprehensive simulation that will be used to help understand and interpret the experimental results.
One-of-a-kind experiments
Stocks explains that all materials have naturally occurring defects and dislocations in their atomic structure. CDP scientists are working to illuminate the types and numbers of defects that result from irradiation, as well as how these induced defects interact with naturally occurring dislocations and microstructural features, such as "grain boundaries" (the areas between grains of metal where defects can gain a foothold) to change the structure of a material and affect properties such as strength and ductility. These phenomena are studied using use x-ray and electron microscopy, as well as nanoscale tests of material's mechanical properties.
"Experimentally, we have two ways to see dislocations," Stocks says. "We are using electron microscopy to provide direct imaging of both single dislocations and clusters of defects. We also have researchers who travel to Argonne National Laboratory to use the tightly focused x-ray beams of their Advanced Photon Source to capture the details of the interaction between a single dislocation and the grain boundary. The idea is that we can use very sophisticated experimental techniques to take snapshots of the process of defect formation at very short time intervals and then use that data to develop a simulation of what we measured. We want to do the same thing in the studies of the interactions between dislocated atoms and grain boundaries."
Insights gained through these studies are used to build computer simulations of the structure of these materials in order to identify the "fundamental events" of both defect production and interactions among dislocations and defects.
"This pairing of experimental and theoretical research on the same length and time scales—or as close as possible—is something that was previously not possible," Stocks says. "We are pushing experiment to ever shorter length and time scales while extending theory and modeling to longer scales—eventually to the point where the two overlap. This allows the most direct comparison between theory and experiment."
Ideally, the computer models will reflect the results of the experiments as closely as possible while providing explanations of the process based on molecular dynamics and quantum theory.
Both of these experimental approaches involve doing things that have never been done before, and neither would be understandable without simulation to back them up. High-performance computers like ORNL's Jaguar and its soon-to-be-online successor, Titan, provide the computational power that enables CDP scientists to try to make a link between complex experimental data and simulations.
High-performance pedigree
To accurately simulate the defect formation process, the CDP will need to develop models that comprise very large numbers of atoms—from tens of thousands to millions. That's a big jump from the hundreds of atoms that have traditionally been possible in calculations based on quantum theory, due to the amount of computing power required to carry them out.
"For most simulation methods that use quantum electronic structure techniques, the amount of computational work required is proportional to the third power of the number of atoms," Stocks explains. "However, beginning in the mid-1990s, we developed methods that scale as the first power of the number of atoms—so N rather than N3."
The combination of the CDP's modeling methods and the extra computational muscle provided by Titan brings the center's goal of "tens of thousands to millions" of atoms just within reach.
"The complexity of these massive simulations is the reason we need high-performance computers," Stocks says.
Roughly speaking, each of the computer's processors handles the calculations for some number of atoms in the simulated system. The more computer cores there are, the more data can be processed in parallel, and the more complex the simulation can be.
"Our method naturally maps onto parallel computers because, when we developed this method in the 1990s, we anticipated massively parallel computer architecture," Stocks says. "Our LSMS (Locally-Self- Consistent Multiple-Scattering) software that models interactions among electrons and atoms in magnetic materials is the first documented example of code that ran on a parallel computer at one teraflop—a trillion calculations per second. A derivative of LSMS, called Wang-Landau, was one of the first codes to get to one petaflop—a thousand trillion calculations per second."
CDP scientists have been working on adapting these and other codes to the rigorously parallel architecture of Titan in anticipation of creating more meticulous defect models than were previously possible.
"When we have the opportunity to apply more computing power to a problem, we have two basic options," Stocks says. "We can do more calculations about a small number of atoms—including calculations of the properties of materials, their stability, and their magnetic structure. Or we can do fewer calculations with many more atoms. For some of the questions we want to answer, the minimum number of atoms we need in order to get an insight into the process is many hundreds of thousands or millions.
Faith in science
To make the most of these experimental insights, over the next few years, Stocks expects that the CDP will apply Titan to the task of creating unprecedentedly detailed simulations of the million or so atoms involved in a radiation damage cascade, at very short time intervals—on the order of trillionths of a second. The simulations will take into account not only the physical movement of atoms within the system, but also the magnetic interactions among the atoms and their myriad electrons.
"Without supercomputers like Titan and Jaguar, we wouldn't even consider doing that," Stocks says.
While acknowledging the potential value of the CDP's findings for the next generation of nuclear power plants, Stocks emphasizes that the goal of the CDP isn't to design a better alloy for use in reactor vessels, but to use experimentation and simulation to understand the defects that underpin radiation damage and the ultimate strength or weakness of materials.
"If we're successful," Stocks says, "the CDP will provide theoretical models that have been validated against experiment and then can be used to guide the development of new materials.
"We have this great faith in science; we believe that if we understand defects in these materials at the most fundamental level, that knowledge will help us to determine what happens in more complex real-world situations. Today radiation-resistant materials are developed largely by intuition, trial and error, and experimentation. We're trying to improve on that by developing a better basic understanding of the defect-formation process." —Jim Pearce