The team’s findings were published as a short communication titled “Linking Lattice Strain and Fractal Dimensions to Non-Monotonic Volume Changes in Irradiated Nuclear Graphite” in the journal Interdisciplinary Materials.
Structural complexities: Graphite has long been used as a vital component of conventional nuclear reactors, and it is expected to continue to be used in future advanced reactors. Graphite is valued in nuclear reactors because its carbon structure serves as a neutron moderator, slowing down the neutrons released by fission reactions so that they are more likely to sustain a chain reaction.
As useful as it is, graphite also contains structural complexities—such as crystalline “filler particles,” a matrix “binder,” and pores of various sizes—that cause the graphite to respond to radiation in unpredictable ways, though it eventually becomes denser before it swells and cracks. This degradation limits the lifetime of the graphite used in nuclear reactors.
The study’s senior author, MIT research scientist Boris Khaykovich, explains, “Graphite deteriorates under radiation, as any material does. So, on the one hand, we have a material that’s extremely well known, and on the other hand, we have a material that is immensely complicated, with a behavior that’s impossible to predict through computer simulations.”

In irradiated graphite, the changing fractal dimensions of porosity are related to its densification and swelling with irradiation damage. The fractal dimensions in turn are related to the Weibull distribution of fracture stress. (Graphic from Khaykovich et al., “Linking Lattice Strain and Fractal Dimensions to Non-Monotonic Volume Changes in Irradiated Nuclear Graphite,” Interdisciplinary Materials; doi.org/10.1002/idm2.70008)
Strong correlation: The investigators studied the microscopic characteristics of irradiated graphite samples obtained from ORNL using an X-ray scattering technique, focusing on the distribution of sizes and surface areas of the pores. These porosity characteristics are known as fractal dimensions.
They found that when graphite is exposed to radiation, its pores initially become filled up with tiny crushed pieces as the material degrades. The porosity then seems to recover in a kind of annealing process in which new pores are formed and grow larger, leading to material swelling. The size distribution of the pores was correlated with the volume changes in the graphite caused by the radiation damage.
According to Khaykovich, “Finding a strong correlation between the [size distribution of pores] and the graphite’s volume changes is a new finding, and it helps connect to the failure of the material under irradiation. It’s important for people to know how graphite parts will fail when they are under stress and how failure probability changes under irradiation.”
Weibull distribution: Based on these findings, the researchers hypothesized that a statistical technique called the Weibull distribution could be used to predict time to graphite failure. This technique has previously been used to predict the probability of failure in other porous materials, including ceramics and metal alloys.
Khaykovich said, "More research will be needed to put this into practice, but the paper proposes an attractive idea for industry: that you might not need to break hundreds of irradiated samples to understand their failure point,” as is necessary today to predict structural failure in graphite.
He also noted that “when you’re building a nuclear reactor, details matter. People want numbers. They need to know how much thermal conductivity will change, how much cracking and volume change will happen. If components are changing volume, at some point you need to take that into account."