(1)
Ceramic materials such as graphite have been considered for fusion power plant applications. General desirable features of graphite include:
1. the abundance and availability of the material.
2. low neutron absorption cross-section and good scattering cross section to moderate energy neutrons.
3. low atomic number (Z = 6) which allows a higher tolerance of the plasma to carbon as an impurity; used in regions which interact with the plasma boundary such as limiters and first walls.
4. high thermal shock resistance which makes it well suited for absorption of thermal pulses which occur with plasma disruptions.
5. chemical inertness and high melting point temperature.
However, the nature of the radiation damage to the graphite lattice places some fundamental limits on its useful lifetime in fusion components. Increasing the crystalline perfection of graphite (with more production cost) is suggested as one method of reducing the damage, but the actual life expectancy of a graphite component in a fusion plant will depend upon the application and in particular to effects such as exposure to neutron dose, level of external stresses and exposure to high energy particles from the plasma (sputtering).
If the neutron dose is considered independently as the limiting feature then it is reasonable to assume that development work might lead to materials of increased life expectancy. It may also be possible to make improvements in the microstructure, such as optimising orientation, grain size and porosity distribution, but the problem with radiation damage in the crystallites seems to persist and may constitute an inescapable limitation.
For irradiation temperatures above 300 C the damage is due to defects which, if removed or decreased in number, will yield higher graphite lifetimes. One way of decreasing the defects (leads to reduced damage) is by using heat treatment but this kind of treatment also reduces the strength of the graphite and makes it more expensive to manufacture. Results have shown that increased life can be obtained in highly orientated pyrolytic carbons, but in artificially manufactured graphites the large internal strains will limit the life to a value dependent on the material, the irradiation temperature and dose.
The best estimate of life expectancy for the best grades of nuclear graphite, based on the loss of physical and mechanical degradation due to fast neutron effects are given in Table 1. The estimated lifetime fluences are based on irradiations in a fission reactor spectrum. The neutron spectrum in a fusion reactor would be considerably harder, with neutron energies up to 14 MeV. The higher energies can potentially produce radiation damage from helium production as well as from atomic displacement due to the effect of several neutron reactions with energy thresholds. Measurements made suggest that the 14 MeV neutrons may be more damaging than displacement calculations would indicate.
GENERAL PROPERTIES - PYROLITIC GRAPHITE [1]
Atomic Properties
Atomic Number : 6
Atomic Radius-Goldschmidt : 0.077 nm
Atomic Weight : 12.011 amu
Photo-Electric Work Function : 4.8eV
Thermal Neutron Absorption
Cross-Section : 0.0034 Barns
Physical Properties
Boiling point : 5000 C
Density @ 20 C : 2.25 g/cm3
Melting point : 3650 C
Electrical Properties
Electrical Resistivity @ 0 C : 1357 u [[Omega]] cm
Cold Junction @ 0 C,
Hot Junction @ 100 C : +0.70 mV
Thermal Properties
Linear Expansion Coefficient
@ 0 - 100 C : 0.6 - 4.3x10-6 m/m-K
Specific Heat @ 25 C : 712 J/kg-K
Thermal Conductivity, @ 0 - 100 C : 80 - 240 W/m-K
Mechanical Properties
Bulk modulus : 33 MPa
Hardness-Vickers : 0.5-1.0 kgf/mm2
Elastic modulus : 4.80 GPa
DATA AND CORRELATIONS
Table 1 shows the variation of structural and thermal properties of pyrolytic graphite with respect to temperature, refs [2,3,4]. Figures 1-4 show the variation of the thermal and structural properties with temperature. Empirical equations for some thermal and structural properties of graphite as a function of temperature are as follows:
Thermal conductivity in W/m-K:
(1)
with the coefficients given as follows:
a b c d e f
1 27.254 -0.1315 2.6678x10-4 2.5522x10-7 1.1277x10-10 -1.825x10-14
2 7700.2 -32.771 6.0693x10-2 -5.4398x10-5 2.2946x10-8 -3.5965x10-12
Specific heat capacity c, in J/kg-K:
(2)
Modulus of elasticity E, in GPa:
(3)
Thermal expansion coefficient [[alpha]], in m/m-K:
(4)
(5)
(6)
(7)
Ultimate tensile strength [[sigma]]u, in MPa:
(8)
with Eqs 1-2 and 4-7 valid in the range 300-3000 K and Eqs 3 and 8 in the range 300-2500 K.
Table 1 Life expectancy of near-isotropic graphite
Temperature C Dose n/cm2 EDN dpa
400 2.9x1022 37
600 1.8x1022 23
800 1.0x1022 13
1000 0.6x1022 8
1200 0.8x1022 14
Table 2 Thermal and structural properties of pyrolytic graphite
T K [[rho] E GPa [[nu]] k1 k2 C [[sigm [[alpha] [[alpha]
] W/m-K W/m-K J/kg-K a]]u ] % ] %
kg/m3 MPa a-dir c-dir
300 2210.0 5.345 0.140 5.700 1950.0 709.0 0.000 0.000
400 5.367 4.090 1390.0 992.0 0.001 0.2717
500 5.400 3.490 1200 1215.2 8.80 0.034 0.5435
600 5.452 2.680 892.0 1406.0 0.117 0.8152
645 5.480 2.450 733.3 1485.2 0.150 0.9375
800 5.596 2.010 667.0 1650.0 0.201 1.3587
1000 5.800 1.600 534.0 1793.0 11.0 0.280 1.9021
1200 6.044 1.340 448.0 1890.0 0.392 2.4456
1500 6.500 1.080 357.0 1974.0 14.0 0.550 3.2608
2000 7.500 0.105 300.0 2130.0 15.0 0.860 4.6195
2500 8.700 0.810 262.0 2190.0 15.0 1.220 5.9782
3000 10.080 0.700 200.0 2230.0 1.600 7.3370
Note: k1 is the thermal conductivity perpendicular to the layers, and k2 is parallel to the layers.
k1 (W/m-K) k2 (W/m-K)
Temperature (K)
Figure 1: Thermal conductivity of pyrolytic graphite both parallel and perpendicular to the layers.
c (J/kg-K) [[alpha]] (10-6 m/m-K)
Temperature (K)
Figure 2: Specific heat and coefficient of thermal expansion of pyrolytic graphite.
Temperature (K)
Figure 3: Elastic modulus of pyrolytic graphite