These are the materials which are used to slow down the speed of fast moving neutrons in a nuclear fission process. It is observed that the fast moving neutrons are not captured by the nuclei of U235 and as a result no fission of U235 would occur. Even the large size of the matter or the mass of the fissionable material does not matter at all. So the neutrons have to be slowed down to restrict them catchable by nuclei of U235. This is done by use of moderators.
The common moderators are graphite and heavy water.
