The mechanical and physical properties of several medium-grained and fine-grained nuclear grade gra­phites currently in production are given in Table 2 (see also Chapter 2.10, Graphite: Properties and Characteristics). The coke type, forming method, and potential uses of these grades are in Table 1. The most obvious difference between the four grades listed in Table 2 is the filler particle sizes. Grade IG-110 is an isostatically pressed, isotropic grade, whereas the others grades shown are near-isotropic and have properties reported either with-grain or against-grain. As discussed earlier (see Section 4.10.2), the orientation of the filler coke particles is a function of the forming method.

The mechanical properties of nuclear graphites are substantially altered by radiation damage. In the unirradiated condition, nuclear graphites behave in a brittle fashion and fail at relatively low strains. The stress-strain curve is nonlinear, and the fracture process occurs via the formation of subcritical cracks, which coalesce to produce a critical flaw.35,36 When graphite is irradiated, the stress-strain curve becomes more linear, the strain to failure is reduced, and the strength and elastic modulus are increased. On irra­diation, there is a rapid rise in strength, typically ^50%, that is attributed to dislocation pinning at irradiation-induced lattice defect sites. This effect is largely saturated at doses >1 dpa. Above ~1 dpa, a more gradual increase in strength occurs because of

structural changes within the graphite. For nuclear graphites, the dose at which the maximum strength is attained loosely corresponds with the volume change turnaround dose, indicating the importance of pore closure and generation in controlling the high-dose strength behavior, and may be as much as twice the unirradiated value.

The strain behavior of nuclear graphites subjected to an externally applied load is largely controlled by shear of the component crystallites. As with strength, irradiation-induced changes in Young’s modulus are the combined result of in-crystallite effects, due to low fluence dislocation pinning, and superimposed structural change external to the crystallite. The effects of these two mechanisms are generally consid­ered separable, and related by

(E/E0) irradiated = (E/Eo)pinning(E/Eo)structure I1]

where E/E0 is the ratio of the irradiated to unirradi­ated elastic modulus. The dislocation pinning contri­bution to the modulus change is due to relatively mobile small defects and is thermally annealable at ^2000 °C. The irradiation-induced elastic modulus changes for GraphNOL N3M graphite37 are shown in Figure 13. The low dose change due to dislocation pinning (dashed line) saturates at a dose < 1 dpa.

The elastic modulus and strength are related by a Griffith theory type relationship.

Strength, st =[GE/nc]l/1 [2]

where G is the fracture toughness or strain energy release rate (J m — ), E is the elastic modulus (Pa), and c is the flaw size (m). Thus, irradiation-induced changes in st and E (in the absence of changes in [G/c]) should follow st/E1/2. High-dose data reported by Ishiyama et a/.38 show significant devia­tion from this relationship for grade IG-110 graphite, indicating that changes in G and or c must occur.

Graphite is a phonon conductor of heat. Therefore, any reduction in the intrinsic defect population causes a reduction in the degree of phonon-defect scattering, an increase in the phonon mean free path, and an increase in the thermal conductivity. In graphite, such thermally induced improvements are attributable to increases in crystal perfection and a concomitant increase in the size of the regions of coherent order­ing upon graphitization. With increasing temperature, the dominant phonon interaction becomes phonon — phonon scattering (Umklapp processes). Therefore, there is a reduction of thermal conductivity with increasing temperature.39 This decrease in the thermal conductivity with increasing temperature can clearly be seen in Figure 14.

The mechanism of thermal conductivity and the degradation of thermal conductivity have been exten­sively reviewed.13,14,26,40 The increase of thermal resis­tance due to irradiation damage has been ascribed by Taylor eta/.41 to the formation of (1) submicroscopic interstitial clusters, containing 4 ± 2 carbon atoms; (2) vacant lattice sites, existing as singles, pairs, or small groups; and (3) vacancy loops, which exist in the graphite crystal basal plane and are too small to have collapsed parallel to the hexagonal axis. The contribution of collapsed lines of vacant lattice sites and interstitial loops, to the increased thermal resis­tance, is negligible.

The reduction in thermal conductivity due to irradiation damage is temperature and dose sensitive. At any irradiation temperature, the decreasing thermal conductivity will reach a ‘saturation limit.’ This limit is not exceeded until the graphite undergoes gross struc­tural changes at very high doses. The ‘saturated’ value of conductivity will be attained more rapidly, and will be lower, at lower irradiation temperatures.42 In graph­ite, the neutron irradiation-induced degradation of thermal conductivity can be very large, as illustrated in Figure 14. This reduction is particularly large at low temperatures. Bell et a/.43 have reported that the room temperature thermal conductivity of pile grade A (PGA) graphite is reduced by more than a factor of 70 when irradiated at 155 °C to a dose of —0.6 dpa. At an irradiation temperature of 355 °C, the room temperature thermal conductivity of PGA was reduced by less than a factor of 10 at doses twice that obtained at 155 °C. Above 600 °C, the reduc­tion of thermal conductivity is less significant. For example, Kelly8 reported the degradation of PGA at higher temperatures: at an irradiation temperature of 600 °C and a dose of — 13 dpa, the thermal conductiv­ity was degraded only by a factor of —6; at irradiation temperatures of 920 and 1150 °C, the degradation was minimal (less than a factor of 4 at —7 dpa). For the fine-grained, isomolded graphite shown in Figure 14, the degradation of thermal conductivity at the irradia­tion temperature (600 °C) was only by a factor of —3, but was by a factor —6 at a measurement temperature of 100 °C.

There are two principal thermal expansion coeffi­cients in the hexagonal graphite lattice; a, the ther­mal expansion coefficient parallel to the hexagonal c-axis and aa, the thermal expansion coefficient par­allel to the basal plane (a-axis). The thermal expan­sion coefficient in any direction at an angle f to the c-axis of the crystal is

a(f) = ac cos2f + aa sin2f [3]

The value of ac varies linearly with temperature from -25 x 10—6K—1 at 300 K to -35 x 10—6K—1 at 2500 K. In contrast, aa is much smaller and increases rapidly from —1.5 x 10—6K—1 at — 300 K to —1 x 10—6K—1 at 1000 K, and remains relatively constant at temperatures up to 2500 K.39

The large anisotropy in the crystal coefficient of thermal expansion (CTE) values is a direct conse­quence of the bond anisotropy and the resultant anisotropy in the crystal lattice compliances. The thermal expansion ofpolycrystalline graphites is con­trolled by the thermal closure of aligned internal porosity which forms as a result of thermal shrinkage strains on cooling after graphitization. Thus, the c-axis expansion of the graphite crystals is initially, partially accommodated by this internal porosity and a much lower bulk CTE value is observed. On further heating, the graphite crystals fill more of the available internal porosity and more of the c-axis expansion is observed. The bulk CTE thus increases with temper­ature (Figure 15).

Figure 15 Temperature dependence of the coefficient of thermal expansion for typical nuclear grade graphite.

Figure 16 The irradiation-induced changes in coefficient of thermal expansion (25-500 °C) for GraphNOL N3M graphite at two irradiation temperatures. From Burchell, T. D.; Eatherly, W. P. J. Nucl. Mater. 1991, 179-181, 205-208.

As the CTE of polycrystalline graphite is depen­dent on the pore structure, irradiation-induced changes in the pore structure (see discussion of structural changes in Section 4.10.4) can be expected to modify the thermal expansion behavior of carbon materials. Burchell and Eatherly37 report the behav­ior of GraphNOL N3M (which is typical of many fine-textured graphites), which undergoes an initial increase in the CTE followed by a steady reduction to a value less than half the unirradiated value of 5 x 10-6 °C-1 (Figure 16). Similar behavior is reported by Kelly8 for grade IM1-24 graphite. Heat energy is stored in the crystal lattice in the form of lattice vibrations. The Debye equation there­fore gives the specific heat, C, as follows:

Figure 17 The temperature dependence of the specific heat of graphite, a comparison of calculated values and literature data for POCO AXM-5Q graphite. Sources: ASTM C 781. Standard Practice for Testing Graphite and Boronated Graphite Materials for High-Temperature Gas-Cooled Nuclear Reactor Components, Annual Book of Standards. ASTM International: West Conshohocken, PA; Vol. 05.05; Hust, J. G. NBS Special Publication 260-89; US Department of Commerce, National Bureau of Standards, 1984; p 59.

C =9RI, 5D

[4]

where R is the gas constant (8.314J mol-1 K-1); T, the temperature; 0D, the Debye temperature; and z = hm/2kT%, where o is the frequency of vibrational oscillations; k, the Boltzmann’s constant; T, the tem­perature; and h is the Plank’s constant.

At low temperatures, where (T/0D) <0.1, z in eqn [4] is large, we can approximate eqn [4] by allowing the upper limit in the integral to go to infinity such that the integral becomes ^(я4/15), and on differen­tiating we get

C = 1941(T / yD)3 J mol-1 K-1 [5]

Thus, at low temperatures, the specific heat is pro­portional to T3 (eqn [5]). At high temperatures, z is small and the integral in eqn [4] reduces to z2dz; hence, on integrating we get the Dulong-Petit value of 3R, that is, the theoretical maximum specific heat of 24.94 J mol-1 K-1. As we are typically concerned only with the specific heat at temperatures above

(Wigner energy) will reduce the effective specific heat (see Section 4.10.4).

1

11.07Г-1-644 + 0.0003688 T0 02191

The electrical resistivity of graphite is also affected by radiation damage. The mean free path of the conduction electron in unirradiated graphite is rela­tively large, being limited only by crystallite bound­ary scattering. Neutron irradiation introduces (1) scattering centers, which reduce charge carrier mobility; (2) electron traps, which decrease the charge carrier density; and (3) additional spin reso­nance. The net effect of these changes is to increase the electrical resistivity on irradiation, initially very rapidly, with little or no subsequent change to rela­tively high fluence.14,37 A subsequent decrease at very high neutron doses is attributed to structural degradation.