A moderator is designed to slow down fast neutrons such that they are more easily absorbed by fissile nuclei. There are two main factors in choosing a moderator:

- The moderator must not absorb neutrons itself. This means it should have a relatively low neutron absorption cross-section.
- The moderator should efficiently slow down the neutrons. Modelling neutron-nuclei collisions as a classical elastic collision, in much the same way as gas molecules are modelled, gives the result that the closer the nucleus’ mass is to that of the neutron, the more energy will be transferred in the collision. This means that lighter elements are favoured.

The following equation shows the fractional energy lost per collision, ξ, on average for a neutron colliding with a nuclide of mass *A*. *E*_{0} is the initial energy of the neutron, and *E*_{s} is the energy after scattering has occurred.

$$\xi = \left \langle \ln \left( \frac{E_{0}}{E_{s}} \right) \right \rangle = 1 - \frac{(A-1)^{2}} {2A} \ln \left( \frac{A+1}{A-1} \right)$$

It is beyond the scope of this TLP to derive this equation, but the basic physics is straightforward. In elastic collisions kinetic energy and momentum are conserved and the energy lost by the neutron can be calculated for any given angle of contact. In three dimensions it is necessary to integrate over all possible angles to obtain an average.

The equation is well approximated by:$$\xi \approx \frac{6}{3A+2}$$

This is good enough for most purposes (to see the error in the approximation click here.). Since this is a classical derivation applied to a quantum situation, there is probably more error due to the original assumptions than this mathematical approximation.

Try out the interactive Flash movie below to see this effect in action. The movie obeys the same physics used to derive the above equations, except in a two-dimensional rather than three-dimensional case. The simulation is meant to show energy lost per collision, and does not give an accurate impression of how often these collisions occur: interatomic distances have been greatly reduced for illustrative purposes. In practice it is the scattering cross-section which determines the *rate* of neutron collisions.

*Note: This animation requires Adobe Flash Player 8 and later, which can be downloaded here.*

Finally, the above analysis can be modified with respect to the neutron cross-sections, by considering the ratio ξ (Σ_{s} / Σ_{a}). This weights ξ with the absorption and scattering cross-sections. The higher this ratio, the more appropriate the material is as a moderator.

## Graphite

Historically, graphite has been a very popular neutron moderator, and is used in the majority of British reactors. However, the graphite used has to be highly pure to be effective. Graphite can be manufactured artificially using boron electrodes, and even a small amount of contamination from these electrodes can make the graphite unsuitable as a moderator since boron is a highly effective neutron absorber, and so it “poisons” the graphite by increasing the overall absorption cross section, Σ_{a}. It also has unique problems: it stores energy in metastable local defects when it is irradiated, particularly at lower temperatures. This so-called Wigner energy can be released suddenly when the graphite spontaneously returns to its stable phase, and this sudden rise in temperature is not desirable since it can cause further structural damage within the reactor. This means that graphite has to be annealed to remove the excess energy in its lattice in a controlled manner. The following Flash movie shows three-dimensional models of the graphite lattice and demonstrates the origins of this metastable phase within the graphite lattice.

*Note: This animation requires Adobe Flash Player 9 and later, which can be downloaded here.*

## Other common choices:

### Light Water

Hydrogen is a good candidate for a neutron moderator because its mass is almost identical to that of the incident neutron, and so a single collision will reduce the speed of the neutron substantially. However, hydrogen also has a relatively high neutron absorption cross-section due to its tendency to form deuterium, and so light water is only suitable for enriched fuels which allow for a higher proportion of fast neutrons.

### Heavy Water

Heavy water has similar benefits to light water, but because its water molecules already have deuterium atoms it has a low absorption cross section. Additionally, because of the high energy of the fast neutrons, an additional neutron might be knocked out of the deuterium atom when a collision occurs, thus increasing the number of neutrons present. The main disadvantage of heavy water as a moderator is its high price.

### Beryllium

Beryllium-9 is favoured, because in addition to being a light element, on collision with a fast neutron, it can react as follows:

^{9}Be + n → ^{8}Be + 2n

The main problems with beryllium are its brittleness as a metallic phase and its toxicity, which make it less favoured as a moderator than the other materials mentioned here.

### Lithium Fluoride

Lithium fluoride is commonly used in molten salt reactors. It is mixed with the molten metal and the fuel, and so its structural properties as a solid are not important.

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