You seem to be asking a question from the first introductory semester. When a fast neutron collides with a reasonably light nucleus, the neutron bounces off slower than it arrived while energy and momentum is transferred to the nucleus. Only slow (thermal) neutrons will initiate further fissions. On the one hand the comparatively heavy carbon (12) is much inferior to hydrogen (1) as in water, on the other hand hydrogen will absorb an appreciable fraction of the neutrons (and become deuterium) while carbon doesn't.

Nuclear graphite is any grade of graphite, usually electro-graphite, specifically manufactured for use as a moderator or reflector within nuclear power reactors. Graphite is an important material for the construction of both historical and modern nuclear power reactors as it is one of the purest materials manufactured at industrial scale and it retains its properties, including strength at high temperatures.

Recent activities in the nuclear industry have exhausted the amount of nuclear-grade graphite available for purchase. Consequently, researchers were required to discover or invent alternative supply(s). Within the spectrum of sources of nuclear graphite, each individual type/source tends to behave in an idiosyncratic manner with each type possessing highly specific attributes which differentiates such types from all other types.

The types of graphite fabricated for use as a neutron moderator in nuclear reactors may be considered nuclear graphite. For nuclear mechanics, a neutron moderator is a medium influencing the behavior of fast neutrons. The medium also may facilitate in morphing fast neutrons into thermal neutrons for producing and sustaining a nuclear chain reaction. Nuclear graphite is also the medium and material comprising neutron reflectors, which reflects neutrons generated in nuclear chain reaction. Other material and elements capable of reflecting neutrons are beryllium, lead, steel, and tungsten carbide.

In the first attempt to produce a self sustaining nuclear reaction, nuclear graphite impurity may have prevented success. The second try was performed with AGX graphite and went critical. The Pile constructed was called the Chicago Pile-1. Interestingly, German scientists reached the conclusion that graphite is preventative when combined with natural uranium for a sustained nuclear chain reaction. However, the scarcity of pure nuclear graphite was at play. The purest nuclear graphite the Germans had access to was a product from the Siemens Plania company. Siemans Plania exhibited a neutron absorption cross section of approximately 7.5 mb. The nuclear graphite used in Chicago Pile-1 portrayed average thermal absorption cross sections of 6.68 mb, 5.51 mb, and 4.97 mb.

To date and for the most part, catastrophic nuclear graphite behaviour such as fusion or crumbling of graphite pieces, has yet to occur despite the fact that large morphological properties are invoked from fast neutron irradiation , which is a safety issue under consideration when nuclear graphite components of nuclear reactors are manufactured and designed. Even with limited theoretical framework (since all safety related effects are not well understood yet), at least one hundred nuclear graphite reactors have operated with relative success over the last 60 years.

Finally, maintaining purity may be considered a safety precaution concerning the integrity of nuclear graphite. Measuring differences in thermal neutron absorption encountered between graphite standards and graphite test bars placed in a reactor is a method for measuring purity and is known as units of in-hours (”delta-in-hours” or DIH). The DIH measurement may be performed at a reactor and is pertinent to graphite utilized as moderator or reflector components of nuclear and test reactors and for thermal columns. The DIH purity value is not negative when a test bar possesses a lower neutron absorption cross section when compared to the standard. The maximum theoretical DIH purity of graphite having a bulk density of 1.70 g/cm/sup 3/ is +1.16. The precision of the method is +- 0.03.

There are numerous types of graphite moderated nuclear reactors currently in operation to produce electricity, including but limited to:

• Gas-cooled reactors (GCRs); these are often moderated with nuclear graphite and CO2 cooled. GCRs possess high thermal efficiency when compared to other reactor types due to increased operating temperatures. There are several operating, yet aging, reactors of this type. GCRs are a thermal neutron reactor design. Decommissioning costs are modern issues pertaining to GCRs.

• Magnox; The Magnox is a now obsolete type of nuclear reactor engineered and remains in use by the UK. The plans and construction were exported to other countries for power plant usage and as a manufacturer of plutonium.

• Advanced gas-cooled reactor;

• Water-cooled reactors;

• RBMK are a Russian reactor built to generate electricity and plutonium. RBMKs are water cooled with a graphite moderator. RBMKs have similarities with the CANDU design inasmuch RMBKs may be refueled while generating power and RMBKs and operate with a pressure tube rather than PWR-style pressure. Numerous safety flaws are associated with the RBMK design with some corrected after the Chernobyl accident where the nuclear graphite caught on fire. RBMK reactors are commonly believed to be among the riskiest designs in use. As of 2010, approximately 11 remain open.

• High temperature gas-cooled reactors. Prismatic concept. The core of a prismatic HTR is assembled from a variety of nuclear graphite components. In prismatic HTR designs graphite components function as neutron moderators and neutron reflectors. During the operations of the prismatic reactor operation graphite components experience complicated stress states. Core designers are currently demanding a theory of failure of nuclear graphite for the prismatic concept.

• The Pebble-bed concept in which NGNP will be a helium-cooled High Temperature Gas Reactor (HTGR) with a large graphite core. Graphite physically contains the fuel, acts as the neutron moderator for this thermal reactor, provides an enormous heat sink for passive safety measures during off-normal (accident) conditions, and comprises the majority of the core volume. The basic technology for inert gas-cooled HTGR design is well established from the early graphite piles of the 1940s to the fully commercial reactor designs operating in the 1980s. These past designs represent the two primary core configurations commercially favored for gas reactors; the solid-block prismatic or the pebble-bed graphite core. While the USA has focused on a prismatic design, active interest in the Pebble Bed design is increasing primarily from the activities of PBMR (Pty.) Ltd. in South Africa. Graphite research for both designs are similar with the pebble-bed core requiring higher cumulative doses and the prismatic core experiencing higher temperatures. What makes PBRs safe is the fuel. PBRs do not employ conventional fuel rods made of enriched uranium. Small pyrolytic graphite coated pebbles with uranium cores are employed instead. As the temperature increases in PBR reactors, the enhanced movement of atoms in the fuel diminishes the probability of neutron capture by U-235 atoms, which is known as Doppler Broadening. Doppler Broadening explains that the nuclei of uranium (under increased temperatures) traverse space more rapidly and in random directions with a broader range of neutron speeds. PBRs have several nuclear graphite constructional zones considered of importance, including but not limited to:

 The active chamber and the moderator of the reactor

 The side reflector(s)

 The top and bottom reflector(s)

 The chamber comprising the reactor where the oscillating field of neutrons is the at a minima and approaching full thermalization – also known as a corner reflector.

 The fuel channel nuclear graphite sleeves. The sleeves envelope the fuel channel and are engineered to occupy spaces between the channel and moderator (e.g. the cylinder around the fuel channel).The fastest neutron flux may be encountered in the fuel channel sleeves.

The design and construction of pebble reactors use pryrolytic graphite, which has traditionally found in the form of bricks due to strength, affordability, and considerable neutron slowing. Pyrolytic graphite proves to sublime at 4000°C. Such amounts are better than twice the approved design temperature of current functioning reactors. Solid rocket nozzles and missile re-entry nose cones are commonly manufactured with unfortified pyrolytic graphite. Unlike the flake waxes and powders in lubricants and pencil lead, pyrolytic carbon burns in air, catalyzed via a hydroxyl radical (extracted from water).

Graphite-moderated reactors at Chernobyl and Windscale are outstanding accidents exemplified the influence of the radical. On the other hand, engineers have professed that high-density pyrolytic carbon is not flammable in air, should the reaction be catalyzed, basing their findings on various research models where water was omitted from the test.

PBRs are temperature controlled with inert gases. The inert gases perform with the nuclear graphite and present a chill effect. PBRs incorporate designs which implement at least one substrate of silicon carbide operating as a fire break, as well as a seal. The fissionables of a PBR are oxides or carbides of uranium, plutonium or thorium which possess melting points greater than other metals. The oxides are incapable of igniting with oxygen, but contain the potential to react, a very high temperatures (according to some studies), via diffusion with nuclear grade graphite. Carbides may combust in oxygen without interfacing with graphite.

For basic knowledge see:

http://www-ns.iaea.org/tutorials/reactor-physics/chapitres/chapters.pdf

For Nuclear grade graphite see:

http://www.tandfonline.com/doi/pdf/10.1080/18811248.1985.9735637

http://www.iaea.org/NuclearPower/Downloadable/Meetings/2012/2012-10-22-10-26-WS-NPTD/Day-3/14.Liang.pdf

Very pure graphite is used in some reactor designs as neutron moderator, though in most cases it is used between and around the fuel, not as part of the fuel itself.

TRISO fuel, which is actually a new kind of fuel that encloses the fissile material into a graphite matrix, is currently under development for some advanced high-temperature reactor designs.

The main reason graphite has been used to date in nuclear reactors, despite the fact that it's not as good a moderator as water (hydrogen), is that it has very low neutron absorption cross section, unlike hydrogen. If graphite is pure enough (without a significant amount of neutron absorbent impurities) and present in sufficient quantity, makes it possible to achieve criticality using just natural uranium as fuel. The latter is not possible with light water. Heavy water would be needed instead, which is much more expensive than graphite.

In summary, graphite moderated reactors are basically the most cost effective option when natural uranium or very low enriched uranium is desired as fuel. If the fuel has a higher enrichment some additional neutron absorption can be afforded. In that case light water can be used both as coolant and moderator, as it happens in most of currently operating reactors.

The ANL answer above is NOT exactly correct. TRISO fuel is NOT new! It has been used at General Atomics' Ft. St. Vrain and German HTGRs. What is "new" is that the US DOE, Idaho National Lab and Oak Ridge National Lab have been working since 2003 to enhance the fabrication, performance, modeling of TRISO fuel and having irradiation tests and PIE done at INL.

TRISO fuel encapsulates the uranium fuel kernels (Pu and mixed oxide kernels are possible) with three layers made of pyrolitic carbon (not graphite per se) and Silicon Carbide. The Pyrolitic Carbide is used for the first and third layer to provide compression for the Silicon Carbide layer which acts an a containment vessel for the kernel's radioactive fission products. Then these trice coated kernels (TRISO) are over-coated with a specific recipe of graphite matrix material and compressed/molded into pellet cylinders or spheres. In the gas-cooled reactor, helium is used for heat transfer, but it is "transparent" to neutrons, in that it is not the moderator. The grapite matrix (prismatic design with cylinders, pebble bed with spheres) acts as the moderator to slow down the fast neutrons generated by fission, to thermal energies, where the uranium fuel has the best neutron absorption. TRISO fuel must use enriched uranium kernels.

Now, for the heavy water reactors, D2O can provide cooling and moderation, and grapite may be used for additional moderation, and natural (unenriched) uranium can be used. In air-cooled, graphite reactors (e.g., Magnox in UK, older AEC reactors at DOE labs) the graphite is the moderator, and natural uranium was used.

http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/32/047/32047840.pdf