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| Fig. 1: Distribution of fission products as a function of mass number. [1] (Courtesy of the DOE) |
Graphite has been used as a moderator in nuclear reactors for over 80 years, since Enrico Fermi initiated the first self-sustaining nuclear chain reaction at Chicago Pile-1 in 1942. [1] Two of the most important nuclear accidents, Chernobyl and the Windscale fire, have occurred in graphite-moderated reactors. Here we shall discuss one of the major design flaws of graphite which led to the latter accident. To contextualize this properly it is necessary to understand the features of an effective moderator and to comparer graphite with other moderators.
In order to understand the role of graphite as a moderator in nuclear reactors, it is necessary to introduce the fundamental principles of a nuclear reaction. The key elements of a nuclear reactor are neutrons, a fissile material for fuel, and a moderator. The most common fuel for nuclear reactors is Uranium, with U-235 used as the fissile atom. In such reactors, fission occurs when a neutron passes near and is absorbed by a U-235 nucleus. The now-unstable U-236 nucleus will break into two fragments each of approximately half the mass, a probabilistic process that creates a distribution of fission products (Fig. 1), a significant release of energy, and the emission of neutrons. Each fission process uses 1 neutron and creates between 2 to 3 neutrons, thereby sustaining a chain reaction. [2]
The neutron moderator plays an integral role in the functionality of a nuclear reactor. In short, the function of a moderator is to slow down the incident neutrons so that they can more efficiently produce fission in the fuel. Why are slower neutrons more effective? As described above, fission occurs when a fuel nucleus absorbs a neutron, with the likelihood of this process occurring described by the fission cross section. The fission cross section increases with decreased neutron speed/energy (Fig. 2); in essence, if a neutron moves slower, it will spend more time in the vicinity of the nucleus, so the probability of interaction between the neutron and the nucleus is higher. The neutron is more likely to scatter off of the nucleus if it is moving too fast. This is where the neutron moderator comes in handy. [3]
There are 3 main features to optimize in choosing a moderator: (1) low mass, (2) large scattering cross section, and (3) small absorption cross section.
Low mass: Since the goal of a moderator is to slow down a neutron as much as possible, we want the moderator to absorb as much of the neutron energy as possible. A quick mechanics calculation via conservation of energy (for elastic collisions) reveals that the mass of the moderator should thus be as close as possible to the mass of the neutron (if they have exactly the same mass, and the moderator is initially at rest, the moderator will absorb all of the neutron energy and the neutron will come to rest). Notably, the average energy decrement caused by a single neutron collision is solely dependent on moderator mass, and a lower mass moderator will cause a larger energy decrement. From this, one can deduce that the number of collisions required to reduce a neutron with some initial energy E0 to thermal energy range (the low temperature range in which fission cross section is high) will be solely dependent on the atomic mass of the moderator and E0. [4]
Large scattering cross section (σs): The scattering cross section can be understood as the probability that a neutron will scatter off of the nuclei of the moderator. We desire the neutrons to be absorbed into the fuel nuclei, not the moderator nuclei, in order to produce fission reactors, hence the need for a large scattering cross section in the moderator.
Small absorption cross section (σa): By equivalent logic, the absorption cross section (probability that a neutron will be absorbed into the moderator nuclei), should be low, to ensure that the neutrons are instead absorbed by the fuel nuclei.
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| Fig. 2: Typical plot of incident neutron energy versus neutron absorption cross section. [1] (Courtesy of the DOE) |
The most effective moderator will optimize all three of these features. In particular, the higher the moderating ratio, given by ξ σs/σa, the more effective the moderator.
Another crucial factor to consider when choosing a moderator is neutron loss during the moderation process. As neutrons lose energy, they pass through an energy region around 100 eV where the absorption cross section of U-238 increases suddenly due to resonance absorption peaks (Fig. 2). It has been shown experimentally that metallic uranium without a moderator cannot sustain a chain reaction unless it is enriched to 6%, since many neutrons are absorbed by U-238 while slowing down. Once we add a moderator, however, most of the space in the reactor is occupied by the moderator, thus inducing fewer neutron collisions with U-238 and therefore less absorption. In particular, the resonance absorption reduction, denoted by the parameter g, in 6%-enriched uranium is approximately 0.511, meaning that only about half of neutrons will survive resonance absorption while slowing down. It can be shown that adding a moderator like graphite will allow nearly all neutrons to survive (g will approach 1) even with very little enrichment. One study, for example, found that highly pure graphite (with boron impurities of approximately 1.5 ppm) in a water-cooled reactor required only 0.7%-enriched U-235 in order to sustain a chain reaction. [5] In this way, moderation helps neutrons avoid resonance absorption, allowing reactors moderated by materials such as graphite or heavy water to operate using natural (unenriched) uranium.
Three of the most common moderators are detailed below, with numerical data corresponding with each moderator provided in Table 1. Note that the values of σs and σa used to obtain the moderating ratio are energy-averaged, since, importantly, both scattering and absorption cross sections are dependent on the energy of the neutrons (with the energy dependence of the latter illustrated in Fig. 2).
Light water: In a light water reactor, neutrons are slowed down by collisions with hydrogen nuclei in water.
Advantages: Since the mass of a hydrogen atom is 1 amu (and the mass of a neutron is approximately 1.00866 amu), H2O is very effective at slowing down neutrons, requiring only 16 collisions to slow down a neutron from 2 MeV to 1 eV. [4] Moreover, light water reactors offer a layer of safety, in that if the reactor overheats, the water will boil away; without a moderator, the chain reaction will stop.
Disadvantages: Regular H2O atoms are prone to absorbing neutrons (large absorption cross section) and forming deuterium, a stable isotope of hydrogen, which has an extra neutron. As a result, it takes more neutrons to sustain a chain reaction with light water. [6] Also, light water reactors require enriched uranium to operate (in order for each fission event to produce enough neutrons to sustain the chain reaction). Natural uranium is a mixture of U-238 and U-235 (about 99% U-238, the non fissile isotope), whereas enriched uranium can be made up of 3.5-4.5% U-235 (the fissile isotope).
Overall: H2O has a moderating ratio of 71. [4]
Heavy water: The moderator is now D2O, and the neutrons are slowed down by collisions with deuterium.
Advantages: Compared to light water, deuterium has a smaller absorption cross section, since an extra neutron has already been absorbed through the creation of deuterium. Heavy water reactors can operate with natural uranium as fuel (less fissile material is required to sustain a chain reaction), eliminating the need for uranium enrichment facilities. An additional benefit arises if incident neutrons knock the extra neutron out of deuterium, increasing the overall population of neutrons that can cause fission.
Disadvantages: Deuterium is quite literally a heavier isotope of hydrogen, as described above, so it is slightly less effective at slowing down neutrons, requiring 29 collisions to slow down a neutron from 2 MeV to 1 eV.
Overall: D2O has a moderating ratio of 5670. [4]
Graphite: With graphite (a crystalline form of carbon) as a moderator, neutrons are now slowed down by collisions with carbon.
Advantages: Graphite-moderated reactors can use natural uranium for fuel, unlike light water reactors. In particular, just like heavy water, graphite moderation will lose fewer neutrons to absorption than light water reactors, meaning more neutrons will be available to be captured by U-238, thus producing more plutonium through breeding. Graphite is also much easier and cheaper to produce compared to heavy water, which requires chemical separation to isolate the heavier isotope.
Disadvantages: Carbon has an atomic mass of 12 amu, so it is much less effective at reducing the energy of neutrons, requiring 91 collisions to slow down a neutron from 2 MeV to 1 eV.
Overall: C has a moderating ratio of 192, in between that of H2O and D2O. [4]
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| Table 1: Neutron data describing the number of collisions needed to reduce a neutron in energy from 2 MeV to 1 eV, as well as the moderating ratio, for 3 different moderators. Note that the cross sections used to calculate the moderating ratios are energy-averaged. [4] |
In order to better understand the usage of graphite-moderated reactors in practice, it is worthwhile to consider a case study. Though the incident at Chernobyl, a graphite-moderated reactor which experienced a runaway nuclear explosion, is one of the most infamous nuclear accidents, this report will focus on the following lesser-known case study, which illustrates one of the design flaws in graphite moderation:
The Windscale Piles were opened in the U.K. in 1950 and 1951, intended to produce plutonium for defense purposes after the United States ended international nuclear collaboration with the Atomic Energy Act of 1946. The Piles used graphite as a moderator and implemented an air- cooling system rather than a water-cooling one, after concerns that a loss of water coolant would require an evacuation zone larger than the land area that the U.K. had allotted. [7] Importantly, the use of air as a coolant would later prove to be a critical factor allowing a graphite fire to occur. Before diving into the specifics of the accident, it is necessary to define a few concepts:
Wigner energy: When carbon atoms, such as those in graphite, are struck by fast-moving neutrons, the atoms may be displaced from their positions in the lattice structure. Displaced atoms create interstitials (atoms occupying a space between regular lattice sites) along with vacancies, although most interstitials will recombine with existing vacancies. [8] However, surviving interstitials and vacancies create defects in the crystal structure of the graphite, termed Frenkel pair defects. Such lattice defects will introduce a stored potential energy known as the Wigner energy. [9]
Wigner release: When a large number of Frenkel defects have accumulated (ie. a large number of atoms have been displaced), they risk unexpectedly releasing their stored energy and thus causing a rapid increase in temperature. This built-up energy can be dissipated by heating the graphite in a process known as annealing, or a Wigner release, in which interstitials will recombine with nearby vacancies. In high temperature reactors, the Wigner release will occur automatically during operation, but low temperature reactors such as the Windscale Piles will accumulate Wigner energy in graphite, necessitating high annealing temperatures. [10]
At Windscale Pile No. 1, the Wigner release was a routine process used in order to periodically release excess heat in the core in a short period of time. [7] However, over time the graphite used in the reactor had likely become increasingly damaged, as reports indicated that annealing became more difficult to accomplish as the graphite in the reactor accumulated more exposure. [10] A fire in the core occurred on October 10, 1957, lasting two days and releasing a dangerous amount of radionuclides. Because the reactor was cooled by air, oxygen was present in the core, allowing the overheated graphite to ignite once temperatures rose sufficiently. One author, Roger Clarke, estimates that the release caused around 100 fatal cancers in the UK. Contradictory reports point to different explanations for the cause of the fire, with the UK government inquiry committee insisting that the annealing operation led to a fire in the fuel. Other evidence seems to indicate that damage to some magnesium-lithium alloy cartridges in the core may have initiated the fire instead. Regardless, the possibility of a graphite-induced accident at Windscale serves as an important warning for implementing graphite moderation in future reactor construction. [7]
The Wigner effect is only one of many changes that can occur due to irradiation in graphite, including but not limited to changes in dimensions, strain, and thermal expansion. [11] Each irradiation effect indicates that extra caution is required in the design of graphite-moderated reactors, and, indeed, only 18 out of 417 operational reactors are moderated by graphite. [12] Still, it remains an important endeavor to strive to understand the physical principles and historical events associated with graphite-moderated reactors.
© Maya Benyas. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] "DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory, Vol. 1," U.S. Department of Energy, DOE-HDBK-1019/1-93, January 1983, pp. 9, 57.
[2] J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, 1991).
[3] Y. Oka, Nuclear Power Reactor Development (Springer, 2025).
[4] W. M. Stacey, Nuclear Reactor Physics, 3rd Ed (Wiley-VCH,2018).
[5] S. E. Turner et al., "Criticality Studies of Graphite Moderated Production Reactors," Southern Science Applications, Inc., Report No. SSA-125, January 1980.
[6] S. Okajima, T. Kugo, and T. Mori, Nuclear Reactor Physics (Springer Tokyo, Tokyo, 2024).
[7] R. Wakeford, "The Windscale Reactor Accident - 50 Years on," J. Radiol. Prot. 27, 211 (2007).
[8] G. B. Engle and B. T. Kelly, "Radiation Damage of Graphite in Fission and Fusion Reactor Systems," J. Nucl. Mater. 122, 122 (1984).
[9] Z.-G. Mei, R. Ponciroli, and A. Petersen, "Wigner Energy in Irradiated Graphite: A First-Principles Study, J. Nucl. Mater. 560, 153663 (2022).
[10] R. P. Wichner and S. J. Ball, "Potential Damage to Gas-Cooled Graphite Reactors Due to Severe Accidents," Oak Ridge National Laboratory ORNL/TM-13661, April 1999.
[11] T. Gellego and T. D. Burchell, "A Review of Stored Energy Release of Irradiated Graphite," Oak Ridge National Laboratory, ORNL/TM-2011/378, September 2011.
[12] "Nuclear Power Reactors in the World," International Atomic Energy Agency, IAEA-RDS-2/45, August 2025.