According to Lee et a/.,43 the effect of neutron irradi­ation on the specific heat of SiC was negligibly small. The specific heat of SiC is therefore assumed to be unchanged by neutron irradiation, although this has not been verified at high dose. A single study5 also indicated that stored energy (Wigner energy) occurs in SiC irradiated in the point defect regime. The relative amount of stored energy appears to be less than that of graphite.44

Because of a low density of valence band electrons, thermal conductivity of most ceramic materials, SiC in particular, is based on phonon transport. For a ceramic at the relatively high temperature associated with nuclear applications, the conduction heat can be generally described by the strength of the individual contributors to phonon scattering: grain boundary scattering (1/Kgb), phonon-phonon interaction (or Umklapp scattering 1/Ki), and defect scattering (1/Kd). Because scattering of each of these types occurs at differing phonon frequencies and can be considered separable, the summed thermal resis­tance for a material can be simply described as the summation of the individual components; that is, 1/K = 1/Kgb + 1/Ku + 1/Kd. As seen in Figure 7, the unirradiated thermal conductivity of SiC is highly dependent on the nature of the material (grain size, impurities, etc.) and the temperature. While materials can be optimized for low intrinsic defect, impurity,

and grain boundary scattering, the temperature — dependent phonon scattering cannot be altered and tends to dominate at high temperature (above about 673 K for SiC).

The effect of irradiation on SiC in the tempera­ture range of ^423-1073 K (the point defect regime) is to produce simple defects and defect clusters that very effectively scatter phonons. For ceramics pos­sessing high thermal conductivity, the irradiation — induced defect scattering quickly dominates, with saturation thermal conductivity typically achieved by a few dpa. Moreover, as the irradiation-induced defect scattering exceeds the phonon-phonon scat­tering, the temperature dependence of thermal con­ductivity is much reduced or effectively eliminated.

The rapid decrease as well as saturation in thermal conductivity of CVD SiC upon irradiation in the point-defect regime has been reported by several authors.8,34,45,52,53 Figure 8 shows this rapid decrease in thermal conductivity for fully dense CVD SiC, including new data, previous data from the authors,52,53 and that of Rohde.45 It is noted that the data of Thorne is omitted as the material was of exceptionally low density for a CVD SiC material. Moreover, the data of Price34 is published with a range of fluence that is not valuable in the figure.

In recent papers by Snead on the effects of neu­tron irradiation on the thermal conductivity of cera — mics,53 and specifically on SiC,16,52 the degradation in thermal conductivity has been analyzed in terms of the added thermal resistance caused by the neutron irradiation. The thermal defect resistance is defined as the difference between the reciprocals of the irradiated and nonirradiated thermal conductivity (1/Kd = 1/Kirr-1/Knonirr). This term can be related directly to the defect type and concentration present in irradiated ceramics.53 Moreover, this term can be used as a tool to compare the thermal conductivity degradation under irradiation of various ceramics or, for example, various forms of SiC. It has been shown that, for certain high purity forms of alumina, the accumulation of thermal defect resistance is very similar even though the starting thermal con­ductivities of the materials are substantially dif­ferent. Similarly, CVD SiC was shown to have a similar accumulation of thermal defect resistance as a hot-pressed form of SiC with substantially lower (^90 W m-1 K~ ) unirradiated thermal conductivity. The utility of this finding is that if the thermal defect resistance is mapped as a function of irradiation tem­perature and dose for a form of high-purity CVD SiC, it can be applied to determine the thermal

conductivity of any high-purity CVD SiC, indepen­dent of the starting thermal conductivity. The accu­mulation in thermal defect resistance generated from the data of Figure 8 is shown in Figure 9.

Another result of the previously reported analysis on irradiated CVD SiC16,52 is that the thermal defect resistance appears to be directly proportional to the irradiation-induced swelling, although the data-set for making the previous assertion was somewhat lim­ited. A compilation plot including the previous data­set as well as the new data of Figure 9 is shown in Figure 10. It is clear from this plot that a linear relationship exists between swelling and thermal defect resistance. Moreover, there does not appear to be any effect of irradiation temperature on this result. The fact that the thermal defect resistance is proportional to the irradiation-induced swelling allows a rough estimate of thermal conductivity. As measurement of thermal conductivity for the SiC TRISO shell is not practical, while measurement of density is routine, this finding allows an indirect determination of thermal conductivity by measure­ment of the density change in the TRISO SiC shell by means of a density gradient column or some other technique.

The thermal conductivity degradation discussed up to this point has been for irradiation temperature associated with the point defect regime. For irra­diation above this temperature (the nonsaturable void swelling regime), the thermal properties are not expected to saturate (at least at low dpa). The primary reason for this is that the formation of voids and other complex defects in the high-temperature regime (which contributes to the unsaturated swelling as seen in Figure 6) contributes to phonon scattering, and these defects will not saturate. Moreover, it has been shown that the linear relationship that existed between swelling and thermal defect resistance (as seen in Figure 10) does not exist in this elevated temperature irradiation regime.16,52 This underlines the fact that the phonon scattering and swelling are not controlled by the same defects in the lower temperature ‘saturable,’ and elevated temperature ‘nonsaturable’ irradiation regimes. A compilation plot of room-temperature thermal conductivity as a function of irradiation temperature for the saturable and nonsaturable temperature regimes is given in Figure 11 .

By comparison to the unirradiated room — temperature conductivity value of ^280 W m-1 K~ ,

Fast neutron dose (x 1025nm-2 E >0.1 MeV)

it is clear that the thermal conductivity degradation in the highest temperature regimes is less dramatic, even though the swelling is rapidly increasing (see Figure 6). This is opposite to the behavior in the lower temperature, saturable regime, where high swelling corresponds to extreme reduction in thermal conductivity. Unfortunately, the data on thermal con­ductivity reduction in the nonsaturable regime is limited, and given the lack of knowledge of the spe­cific defects governing the phonon scattering, it is not possible to accurately predict behavior outside of the data-set of Figure 6.

Data presented thus far has been limited to mea­surement of thermal conductivity at room tempera­ture. As described in Figure 7, there is a dramatic dependence of thermal conductivity on measure­ment temperature. The temperature dependence of irradiated materials can be found by applying the temperature dependence of unirradiated SiC (the Umklapp thermal resistance term) to the as-neutron-degraded room-temperature values. This approximation (dashed lines) is compared to actual
data (solid lines) in Figure 12 and shows fair corre­spondence. However, it is clear that such a treatment systematically underestimated the thermal conduc­tivity degradation. This implies temperature depen­dence on the defect scattering that is not presently understood.