4. A graphite component in a nuclear reactor at 300C is subjected to a neutron spectrum given by the following equation:

(En)=10¹³ + 4/9 10¹¹ [En(keV) 100] [n/cm2.s.keV]

The minimum and maximum neutron energies are 100 keV and 1 MeV.

a. Using the NRT model, find the number of dpa/s due to collisions of fast neutrons with atoms in the solid. Take Ed=25 eV and assume that the scattering cross section is independent of energy and equal to 2 barns, such that s(E_n, E) = 2 barns/E_n. Also, integrate the displacement cross section over T_dam from 0 to En. (10 points)

b. It is given that the saturation point defect (Frenkel pair) concentration is 5 x 10^-3. How long will it take for this concentration to accumulate assuming no recombination or annealing (i.e. irradiation takes place at 0 K)? How long will it take for 1 dpa to accumulate? (10 points)

c. The samples are then heated so the Frenkel pairs annihilate. Calculate the energy released (J/cm³) in the recombination of all Frenkel pairs from graphite which contains the saturation point defect concentration from b) if the formation energy of the vacancies is 5 eV and that of interstitials is 7 eV, given that the density of graphite is 2.2 g/cm³. You will need to compute the number of Frenkel pairs per volume and multiply it by the formation energies. (10 points)

d. Calculate the resulting temperature increase, assuming adiabatic conditions at the surface of the graphite block (E = c_pT), if the heat capacity of graphite is 0.71 J/gK. Why arent large temperature increases like this observed in reactor? (10 points)