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Origins of Wigner Energy in Graphite
Graphite is the most common allotrope of carbon found in nature, and is often used as a neutron moderator.

Upon irradiation Wigner energy builds up inside the graphite lattice. The mechanism by which Wigner energy is created and released is still not well understood, but the generally accepted view is that the graphite forms a metastable phase due to point defect generation, and if many point defects are formed then the graphite can spontaneously return to its stable phase, giving off energy in the process.

This animation shows the graphite lattice, and the possible point defects that can form within it, as a three-dimensional model. The mouse can be used to rotate the models.
Origins of Wigner Energy in Graphite
First, consider a section of a perfect graphite lattice, consisting of two layers (for clarity one layer is shown in blue and the other in green):
The solid lines represent covalent bonds between the carbon atoms, and the red lines between layers are show how the layers line up with respect to each other. The layers are 0.335 nm apart, and are bonded together electrostatically.
Bond length = 0.143 nm
Drag to rotate the lattice.
Origins of Wigner Energy in Graphite
As with any irradiated material, Frenkel defects are formed within the graphite lattice. This gives rise to vacancies, an example of which is shown below where two vacancies are present.
As can be seen, some of the atoms are now only twofold co-ordinated, allowing the creation of an extra bond (shown here as red translucent line) between the graphite layers, along with a slight change in bond angles of existing bonds. The other twofold co-ordinated atoms in each layer form a weak reconstructive bond with each other (not shown).
Bond length = 0.143 nm
Drag to rotate the lattice.

Origins of Wigner Energy in Graphite
On formation of vacancies, the atom that previously occupied that lattice site now becomes a self-interstitial atom. This atom can lie between layers, such as the "spiro"-interstitial shown below.
This interstitial atom is fourfold co-ordinated, and does cause some local lattice distortion since a fourfold co-ordinated carbon atom is more stable in a tetrahedral conformation. The layers are no longer completely coherent; there is some basal shift. These two defects shown are just some of many possible in the graphite lattice.
Bond length = 0.143 nm
Drag to rotate the lattice.

Origins of Wigner Energy in Graphite
When the interstitial atom and the vacancy are close enough to each other to easily recombine, the defect is referred to as an intimiate Frenkel pair defect as shown below.
In this case, a recombination would occur when both purple bonds break, and allowing new bonds to form to restore the perfect lattice. An energy barrier must be overcome to break the purple bonds, and this is why Wigner energy release requires a large temperature, at around 200°C. If there is a large population of interstitials, many recombinations can happen very quickly at this temperature, and since each recombination releases 13-15eV there is a large temperature spike in the lattice.
Bond length = 0.143 nm
Drag to rotate the lattice.

Origins of Wigner Energy in Graphite
This photo shows a British nuclear reactor at Windscale (now Sellafield). In 1957, the core of a reactor there caught fire causing one of the world's worst nuclear accidents at that time. When the core temperature was observed to be rising suddenly it was assumed that Wigner energy release was occuring, so the graphite was annealed (heated) to restore the lattice to its stable state and release the energy it stored in a controlled manner. However, the reactor was not designed with the annealing process in mind due to a lack of understanding of Wigner energy at that time. This meant that hot spots in the core were unknowingly created, which set fire to the metallic uranium then used as a fuel. One of the reasons that uranium dioxide is now commonly used instead of uranium is because it avoids this risk of fire.