It would not be appropriate to continue without some discussion on stored (or Wigner) energy. The perfect crystal configuration is the lowest energy state for the graphite lattice. However, irradiation damage will considerably alter that configuration. Wigner38 predicted that the increased lattice vibra­tion due to heating would allow carbon atoms to rearrange themselves into lower energy states, and that in doing so energy would be released in the form of heat. Early experience in operating graphite­moderated plutonium production and research reac­tors at low temperatures in the United States, Russia, France, and the United Kingdom proved that this assumption was correct. The highest value of stored energy measured was ^2700Jg-1.15 If all of this were released under adiabatic conditions, the temperature rise would be 1500 °C. Fortunately, that is not the case. Furthermore, the accumulation of stored energy is insignificant above an irradiation temperature of ^300 °C, it is difficult to accidentally release the stored energy above an irradiation

Displacement cascade

Vacancy

loop /———— v

____________ v

Figure 15 Formation of interstitial and vacancy loops in graphite crystals. Modified from Simmons, J. Radiation Damage in Graphite; Pergamon: London, 1965.

temperature of ~-150 °C, and only limited self-sus­taining energy release of stored energy can be achieved in graphite irradiated below ^100 °C. Thus, stored energy is now of consideration in the United Kingdom only in the decommissioning of shutdown reactors such as the Windscale Piles and BEPO and other similar overseas systems, although there are graphite ‘thermal columns’ in some research reactors that may require periodic assessment.

The reason for this is the nature of the irradia­tion damage sites with respect to irradiation tempera­ture. In graphite irradiated in the early facilities,
at temperatures between about ambient and 150 °C, point defects associated with Frenkel pairs and small loops can diffuse only slowly through the lattice to form larger, more stable loops because of the low irradiation temperature. However, thermal annealing at temperatures above the irradiation temperature can readily release the stored energy, and under certain circumstances, this release can be self-sustaining over certain temperature changes. (A ‘rule of thumb’ tem­perature of 50 ° C above the irradiation temperature is often cited as a ‘start of release temperature.’ How­ever, this is misleading as a heat balance needs to be

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Figure 16 The accumulation of stored energy as a function of fluence and temperature.

considered when assessing energy release rates. Thus, 50 °C above the irradiation temperature can be con­siderably overconservative.)

The accumulation of stored energy, measured by burning irradiated graphite samples in a bomb calo­rimeter, is given as a function of fluence and temper­ature in Figure 16. At low fluence, stored energy quickly accumulates reaching a plateau at high flu­ence. Many measurements were made in the Wind — scale Piles, BEPO, Hanford, and Magnox reactors that clearly illustrated this behavior.15

To fully understand the thermal stability of graph­ite containing stored energy, the most appropriate measure is the rate of release of stored energy measured using a differential scanning calorimeter (DSC) as illustrated in Figure 17.

A graphite sample is heated in the DSC usually at a constant rate of 2.5 °Cmin~ In simple terms, two runs are made and the heat capacity of the samples measured in each case. When the heat capacities from the two runs are subtracted, the energy release rate is easily obtained as a function of heating temperature. This can be compared to the specific heat of graphite as given in Figure 17. When the rate of release of energy is below the specific heat, energy needs to be added to continue the process. When the rate of release is above the specific heat, the process is self-sustaining. This behavior was used to ‘anneal’ the Windscale Piles; a ‘hit and miss’ strategy that ended in damage to the fuel cartridges and eventually a
‘metal uranium fire.’ (Contrary to ‘common folklore,’ the graphite did not burn in the Windscale incident. A limited amount of graphite was oxidized leading to enlargement of fuel and control channels but it was the metal uranium that burnt. Graphite is very diffi­cult to burn and requires large amounts of heat and oxygen or air, applied to crushed graphite in a flui­dized bed or in similar form.39)

The form of this rate of release curve is a func­tion of (1) the amount of stored energy in the sample, (2) the temperature the sample was irra­diated at, (3) the fluence the sample had been irradiated to, (4) the release temperature, and (5) the heating rate. Unfortunately, there are no com­prehensive datasets of these five parameters that allow a robust empirical model to be derived for assessing the stability of graphite containing stored energy. The models that usually exist take the worst — case rate of release curve and fit an Arrhenius type equation to the rate ofrelease curve.

where S is the stored energy remaining, t is time, T(t) is temperature in (K) as a linear function of time (T = at in the case of the DSC test and is nonlinear in most practical cases), Kis Boltzmann’s constant, and E(T S) is the activation energy as a function of the stored energy remaining and temperature and u is a frequency factor usually taken as 7.5 x 1013 s~140

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It can be appreciated that the exact solution of eqn [30] requires a substantial amount of information from several rate of release curves from several samples, which is seldom available. Thus, a practical approach is usually taken, the simplest of which is to assume a single activation energy. However, this is not very satisfactory and more elegant approaches using vari­able or discrete activation energies can be found.41- Having derived a satisfactory model for the rate of release using a DSC, it then can be applied to a practi­cal situation using commercially available computer codes such as ‘user subroutine’ facilities.42

In assessing practical situations, it is important to use an energy balance that accounts for heat applied, heat generated by the release of stored energy, the heat capacity of the graphite itself, and heat lost to the surroundings. If the heat generation is intense and oxygen is available, the heat generated by graphite oxidation should be taken into account. However, the latter case should be unnecessary as a professional scientist or engineer would not design a system or process that would approach such conditions. It should be noted that irradiated graphite thermal conductivity and total stored energy are directly cor­related15; see eqn [31]. Therefore, the thermal con­ductivity will improve as energy is released.

1 Jg-1

The data that eqn [30] is based on is derived from rate of release curves obtained using a relatively fast heating rate. In dealing with irradiated graphite waste, much slower rates of heating are often required. Graphite samples taken from the Windscale Piles 40 years after the incident showed little change in the dS/dt curves,45 indicating that diffusion of atoms at around ambient temperature is extremely slow. Nevertheless, condi­tions relevant to any proposed encapsulation technique and repository will need to be accounted for in deter­mining if heat released from stored energy is an issue.

The rate of release curves given in Figure 17 are only to a temperature of around 450 °C. It had been observed, by comparing the energy released in the DSC with the energy released on a similar sample in a bomb calorimeter, that not all of the stored energy had been released in the samples heated to a maxi­mum of 450 °C in the DSC. It was found that on increasing the temperature to around 1600 °C, a sec­ond peak could exist46,47; see Figure 18.

It was observed that the ‘200 °C’ peak reduced in size and moved to a slightly higher temperature with increased irradiation, presumably as the irradiation induced defects became more stable, and the plateau between the two peaks increased in height and approached the specific heat value.15 The first of these phenomena could explain why it became more and more difficult to ‘anneal’ the Windscale Piles39 and the second had the implication that

eventually the rate of release curve would remain above the specific heat up to 1600 °C with the conse­quent safety implications. Fortunately, the second of these phenomena proved to be incorrect.

It is interesting to note that there is a correla­tion (eqn [32]) between the height of the plateau at ^400 °C and total stored energy.15

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This equation, although not exact, was often used in reactor graphite sampling programs to avoid having to measure total stored energy.

Most of the discussion on stored energy above is relevant only to low temperature reactor systems, with graphite temperatures operating from ambient to 150 0C. When graphite is irradiated at higher tem­peratures, in practice above about 100 0C, the dS/dt does not exceed the graphite specific heat. One of the operating rules for the UK Magnox reactors was that the dS/dt, as measured on surveillance samples, should always be below 80% of the specific heat, which proved to be the case.