Fast neutron irradiation and, in the case of car­bon dioxide-cooled reactors, radiolytic oxidation change many of the properties of graphite. The

properties of interest to the nuclear engineer are

the following:

• Stored energy — a function of fast neutron damage and temperature, due to damage to the graphite crystallites, but not affected by radiolytic oxidation other than by a reduction in mass.

• Specific heat — a function of temperature but not affected by fast neutron irradiation or radiolytic oxidation other than by stored energy, which may be considered separately.

• Dimensional changes — a function of fast neutron damage and irradiation temperature. There is also some evidence of modification by radiolytic oxida­tion. It is also modified by stress (see irradiation creep).

• CTE — a function of temperature, fast neutron damage, irradiation temperature, and stress. There is evidence that it is not modified by radio­lytic weight loss.

_ 30

28

26 c

24

(Л

22

$

20 E

18 .c

16

14

о

12

о

° 10 ————- ,——— ,———- ,——— ,———- ,——— ,——— ,———- ,

0 2 4 6 8 10 12 14 16

Fluence (1020 ncm-2 EDND)
c-axis

Fluence (1020 ncm-2 EDND)
a-axis

♦ 150 °C ■ 170 °С A 200 °С • 250 °C

Figure 22 Low-temperature changes to coefficient of thermal expansion in highly orientated pyrolytic graphite. Modified from Kelly, B. T.; Martin, W. H.; Nettley, P. T. Philos. Trans. R. Soc. Lond. A Math. Phys. Sci. 1966, 260(1109), 37-49.

• Thermal conductivity — a function of temperature, fast neutron damage, and irradiation tempera­ture. It is significantly modified by radiolytic weight loss.

• Young’s modulus — a function of temperature, fast neutron damage, and irradiation temperature. It is significantly modified by radiolytic weight loss.

• Strength (tensile, compressive, flexural, and frac­ture) — a function of temperature, fast neutron damage, and irradiation temperature. It is signifi­cantly modified by radiolytic weight loss.

• Electrical resistivity — a function of temperature, fast neutron damage, and irradiation temperature. It is probably modified by radiolytic weight loss.

• Irradiation creep — a function of fast neutron dam­age, irradiation temperature, and stress.

These property changes are illustrated in Figure 30.

These dimensional changes, property changes and creep mechanisms are correlated, some more strongly than others. This has been taken advantage of in various semiempirical models for irradiation damage in graphite.57-60

In discussing the irradiation behavior ofpolycrystal — line graphite, it is useful to split these changes into low, medium, and high fluence effects. At low irradiation, fluence changes in polycrystalline graphite are strongly correlated with the crystallite changes discussed else­where; see Section 4.11.11. Typical mechanisms would

_ 30

the accumulation of stored energy, pinning (leading to a rapid increase in Young’s modulus), and the rapid decrease in thermal conductivity. At medium fluence, several of the properties saturate, such as Young’s mod­ulus and thermal conductivity. At high fluence, when crystallite growth in the ‘c’ direction has taken up much of the accommodation provided by Mrozowski cracks,11 and larger ‘cracks,’ the polycrystalline struc­ture starts to become strained, thereby generating new cracking. At extremely high fluence, beyond that expe­rienced in a modern power production reactor, the crystallite swelling becomes so large that the polycrys­talline structure completely breaks down leading to a rapid decrease in modulus and strength.

Each of the property changes is discussed in more detail below. In attempting to understand the behavior of polycrystalline graphite, reference is made to the irradiation behavior of HOPG, as previously discussed in Section 4.11.11. This is because HOPG is considered to be a representative model material for the individual crystallite structures in polycrystalline graphite.

4.11.10 Averaging Relationships

Before looking at each of the properties individually, it is first worth considering the methods developed to relate changes in the crystallites to the bulk

♦50 °C ■ 150°C » 650°C • 1000°C
0.5	1.0	1.5	2.0	2.5

Fluence (1020 ncm-2 EDND)

Figure 24 Reduction in C33 in irradiated highly orientated pyrolytic graphite. Modified from Seldin, E. J.;

Nezbeda, C. W. J. Appl. Phys. 1970, 41(8), 3389-3400; Summers, L.; Walker, D. C. B.; Kelly, B. T. Philos. Mag. 1966, 14(128), 317-323.

_ 5 E

4

И

o’ 3

CO

1 2

О

E

1

CO

_cc

Ш

0

50 °C

_ 0.5

E

0.3

от

0.2

о

E

0.1

to

_ra

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fluence (1020 ncm-2)

650 and 1000 °C

Figure 25 Changes in C44 with irradiation in highly orientated pyrolytic graphite. Modified from Seldin, E. J.; Nezbeda, C. W. J. Appl. Phys. 1970, 41(8), 3389-3400.

properties of polycrystalline graphite. In the 1960s, Simmons derived a model based on the following assumptions: polycrystalline graphite could be con­sidered to be a single phase, porous aggregate of
identical crystals with the correct graphite symmetry, and small element volumes containing only graphite could be chosen so that their internal and external stress could be considered to be uniform.61

From first principles and by applying the laws of thermodynamics for the assumptions given above, Simmons derived the following relationship for the bulk dimensional change rate:

, dxc, , .

Ax^—h(1 _ Ax) dg

where dexx/dg, dxc/dg, and dxa/dg are the linear dimensional change rate in polycrystalline graphite in some direction V and the crystallite dimensional change rates in the ‘a’ and V directions respectively. Simmons also derived the following relationship for the bulk CTE:

axx Axac ^ (1 Ax)aa [34]

where axx, ac, and aa are the linear CTE in poly­crystalline graphite in some direction ‘x’ and the crystallite CTE in the ‘a’ and V directions, respectively.

The so-called structure factor ‘Ax’ is the summa­tion rate of change in rate of the crystallite stresses with respect to the change in bulk stress, as illustrated in the equations below.

0 50 100 150 200 250 300

Fluence (1 020 ncm-2 EDND)

Figure 26 Changes in the thermal conductivity of highly orientated pyrolytic graphite. (a) Change in thermal conductivity in the ‘a’ direction as a function of fluence, (b) Change in thermal resistance as a function of temperature, and (c) Normalized change in thermal resistivity as a function of irradiation and measurement temperature. Reproduced from Taylor, R.;

Kelly, B. T.; Gilchrist, K. E. J. Phys. Chem. Solids 1969, 30, 2251-2267.

(1 ) = Qs (°22,п + ^ll,»^

For a more detailed derivation of these equations see Hall et al61

In addition, Simmons4 provided evidence that there is a linear relationship between unirradiated CTE and initial dimensional change rate for poly­crystalline graphite (Figure 31). Brocklehurst and Bishop62 later found a similar relationship in bromi — nated graphite.

Expressions to those of Simmons have been derived by Sutton and Howard12:

«par = K1g « + K2baa

«perp K3gac ^ K4b«a [36]

where K1, K2, K3, K4, g, and b are crystal accommoda­tion and Bacon13 crystal orientation factors. A similar but more complex relationship was also derived by Jenkins.63 In the discussion of the individual
properties, the anisotropic graphite PGA and the semi-isotropic Gilsocarbon graphite are used as examples.