CFCs for fusion applications are specifically designed to maximize thermal conductivity and for this reason irradiation-induced thermal conductivity degradation
is of primary importance. As with ceramics, graphite thermal conductivity is dominated by phonon trans­port and is therefore greatly affected by lattice defects, such as those caused by neutron irradiation. The extent of the thermal conductivity reduction is therefore directly related to the efficiency of creating and annealing lattice defects, and is therefore related to the irradiation temperature.

The effect of neutron irradiation on the thermal conductivity of graphite has been widely studied. The majority of the literature10, , — 1 in this area has been in support of the gas-cooled, graphite-moderated, fission reactor program in the United States and United Kingdom and has focused on ‘nuclear’ gra­phites as well as more fundamental work on pyrolytic graphite.8,27,32,33 In recent years, the emphasis of graphite radiation effects research has switched to its use in PFCs of graphite fusion reactors.10,11,34

Because of the significant advances in carbon — carbon composite (CFC) processing and fiber develop­ment, very high thermal conductivity materials have been recently demonstrated and they have become attractive for high heat flux applications. The highest thermal conductivity CFCs are made from highly crys­talline graphite fibers having intrinsic conductivities approaching those of pyrolytic graphite. For example, vapor-grown carbon fibers35 have a thermal conductiv­ity of 1950 W m-1 K- . Along with advances in fiber properties, improvements have occurred in both mono­lithic graphite and the CFC matrix-processing areas, which also have enhanced thermal conductivities.

The physical processes governing the thermal conductivity of graphites, as well as the mechanisms responsible for the radiation-induced degradation in conductivity, are well established.8 For all but the poorest grades of carbon, thermal conductivity is dominated by phonon transport along the graphite basal planes and is reduced by scattering ‘obstacles’ such as grain boundaries and lattice defects. For graphites with the largest crystallites, that is, pyro­lytic graphite or natural flake, the in-plane room temperature thermal conductivity is approximately 2000 W m-1 K-1.36

The thermal conductivity of graphite-based mate­rials can be written as a summation of the thermal resistance due to scattering obstacles:

K (x) = b(x)

where b(x) is a coefficient that includes terms due to orientation (with respect to the basal plane), porosity, and some other minor contributors. This coefficient
is assumed in most cases to be constant with tem­perature, with a value of around 0.6. The first two terms inside the parentheses are the contributions to the thermal conductivity due to umklapp scattering (Ku) and grain boundary scattering (Kgb). The grain boundary phonon scattering dominates the thermal resistance (1/Kgb) at low temperatures and is insig­nificant above a few hundred degrees Celsius, depending on the perfection of the graphite. The umklapp scattering, which defines the phonon — phonon scattering effect on the thermal conductivity, dominates at higher temperatures and scales nearly as T2.8 The umklapp scattering therefore defines the upper limit to the thermal conductivity for a ‘perfect’ graphite. Following Taylor’s analysis,37 the umklapp — limited thermal conductivity of the graphite crystal would be ^2200Wm~1K~1 at room temperature, in close agreement with the best pyrolytic graphites or the vapor grown carbon fibers mentioned earlier.

The third term in eqn [7], Kx, is the contribution to the basal plane thermal resistance due to defect scattering. Neutron irradiation causes various types of defects to be produced depending on the irradia­tion temperature. These defects are very effective in scattering phonons, even at flux levels that would be considered modest for most nuclear applications, and would quickly dominate the other terms in eqn [7]. Several types of irradiation-induced defects have been identified in graphite. For irradiation tem­peratures lower than 650 °C, simple point defects in the form of vacancies or interstitials, along with small interstitial clusters, are the predominant defects. Moreover, at an irradiation temperature near 150 °C,27 the defect that dominates thermal resistance is the lattice vacancy.

Due to its sensitivity to the presence of defects, the temperature at which graphite is irradiated has a profound influence on the thermal conductivity degradation. As an example, Figure 15 shows one of the most complete sets of irradiation data on Pile Grade A nuclear graphite.38 This graphite is a medium­grained, extruded, anisotropic material with a room temperature thermal conductivity of 172 W m—1 K— in the extrusion direction. Figure 15 presents the normalized room temperature thermal conductivity of this graphite of various irradiation temperatures. It is seen that as the irradiation temperature is decreased, the degradation in thermal conductivity becomes more pronounced. For example, following irradiation at 150 °C, the thermal conductivity of this graphite appears to approach an asymptotic thermal conductivity of ~1% of the original. The reason for

this is that as the irradiation temperature is decreased, the fraction of vacancies surviving a cascade event increases, and thus the number of vacancies available to scatter phonons is much higher for the lower temperature irradiation.

Data have been published for CFCs whose thermal conductivities are similar to those of nuclear graphites, showing degradation similar to that expected from the graphite literature. For example, Burchell34 has shown that the saturation thermal conductivity for a 3-directional composite (FMI-222, Kunirr = 200 W m—1 K—1 at RT) is reduced to ^40% of the origi­nal room temperature conductivity following fast neutron irradiation at 600 °C. Published data for the degradation of thermal conductivity in highly con­ductive CFCs have led to the conclusion that a higher initial conductivity composite results in higher abso­lute conductivity after irradiation.39,40 Figure 16 demonstrates this point. At the extremely damaging irradiation temperature of 150 °C, it is observed that the absolute reduction (lunirr — Kirr) is substan­tially greater for the high thermal conductivity mate­rials compared to the lower conductivity CFCs and graphite, as seen in Figure 16, although the normal­ized fraction (Kirr/Kunirr) is approximately the same for all the carbon materials in the figure. Moreover, saturation in thermal conductivity degradation occurs at a neutron dose of ~1 dpa. Data for higher irradia­tion temperatures11, 1 show that the higher thermal conductivity materials have a slightly larger fractional
change in thermal conductivity (Kirr/Kmirr) compared to lower conductivity materials, although the absolute value of the irradiated thermal conductivity is still greater for the higher conductivity materials. A com­parison of thermal conductivity degradation for a nuclear graphite (CH-45) with the composites FMI-222 and MFC-1 is given in Figure 17.31

For the low-dose regime relevant to machines such as ITER (less than 1 dpa or about 500 h in this figure), the conductivity is seen to decrease by a factor of two for the highest conductivity material (MFC-1) and by about 30% for the nuclear graphite.

An algorithm has been developed to predict the thermal conductivity degradation in a high thermal conductivity composite (^555Wm~1K~1 at room temperature) as a function of radiation dose and temperature.41 The absence of irradiation data on CFCs of this type required the use of data from intermediate thermal conductivity materials and pyrolytic graphite to derive an empirical radiation damage term.24,2728,39,42

An analysis of the effects of temperature and neu­tron dose on the thermal conductivity is shown in Figure 18. Specifically, the algorithm assumed the nonirradiated properties of the unidirectional fiber composite MFC-1 material compiled with an empir­ical radiation damage term. As with the experimental data of Figures 15 and 16, it is seen in Figure 18 that an enormous loss in thermal conductivity occurs at low irradiation temperatures. Presently, only a few data points exist that are relevant to the validation of this algorithm, and these are also plotted on the figure.39 The data do agree within the errors of irradi­ation temperature and thermal conductivity measure­ment, with the algorithm predictions. However, they

Time in reactor (h) Time in reactor (h)

1-3dpa irradiation

Figure 19 Effect of neutron irradiation on thermal conductivity-driven temperature evolution in a monoblock and flat-plate divertor design.

are insufficient to validate the algorithm and the need clearly exists for additional data for this purpose.

To illustrate the usefulness of such an algorithm, and the significance of the issue of thermal

conductivity degradation to the design and operation of PFCs, this algorithm has been used to construct Figure 19, which shows the isotherms for a mono­block divertor element in the nonirradiated and

irradiated state and the ‘flat plate’ divertor element in the irradiated state. In constructing Figure 19, the thermal conductivity saturation level of the 1 dpa given in Figure 18 is assumed, and the flat plate and monoblock divertor shown are receiving a steady state flux of 15 MW m~ . Both composite materials have been assumed to be in perfect contact with a copper coolant tube or plate. Figure 19 clearly shows two points. First, a very high conductivity composite is required to handle the extreme heat fluxes expected if the temperature is to be limited to <1200 °C (Section 4.18.4). Second, the effect of neutron irra­diation on the temperature is significant. In the case of the flat plate divertor, the temperature rise (AT) changes from ^200 to ^500 °C following irradiation, while for the monoblock, it increases from ~-350 to ^900 °C. It should be noted that the larger tempera­ture increase for the monoblock design is due not to the larger path length of graphite in that configura­tion, but rather to the larger amount of graphite material that is irradiated in the highly damaging low temperature regime (see Figures 15 or 18). The larger temperature increase for the monoblock design could be unacceptable from an erosion stand­point, as will be discussed in Section 4.18.4.

Because of the serious thermal conductivity deg­radation in graphite, scenarios to limit the issue (such as baking the PFM) have been considered. Upon annealing above the irradiation temperature, some interstitial atoms become mobile and can recombine with vacancies, restoring the thermal conductivity of the lattice. It is therefore conceivable that intermit­tent annealing of the PFC could regain some of the irradiation-induced thermal conductivity degradation. Bake-outs are typically conducted between operating cycles of a fusion system for plasma impurity (usually oxygen) control. However, the wall-conditioning temperatures are typically limited to less than 300 °C and for various reasons cannot be significantly increased. Inspection of data such as those given in Figure 2041 indicates that little recovery in thermal conductivity is possible unless bake-out temperatures approach 1000 ° C, and thus in situ annealing can be of only marginal benefit.