Activation Energy for Annealing Single Interstitials in Neutron-Irradiated Graphite and the Absolute Rate of Formation of Displaced Atoms

Abstract

The activation energy for the process of annealing single interstitials in neutron-irradiated graphite and the absolute rate of formation of displaced atoms have been determined experimentally from both the dimensional expansions and $c$-axis expansions of graphite irradiated at temperatures between 77\ifmmode^\circ\else\textdegree\fi{}K and 490\ifmmode^\circ\else\textdegree\fi{}K. The activation energy obtained is 0.068 to 0.074 eV and lies between the value of 0.1 eV estimated by Dienes and the value of 0.016 eV calculated by Iwata, Fujita, and Suzuki for the migration energy of a single interstitial.The absolute rate of formation of displaced atoms corresponds to the rate of displacement when no annealing occurs during the irradiation process. The value obtained (5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$% displaced atoms/MWD), is 2.5 times the rate of displacement at 30\ifmmode^\circ\else\textdegree\fi{}C and is in excellent agreement with theoretical estimates.The dimensional changes occurring during the first irradiation of graphite are the result of the three processes: $(1) \ensuremath{\varphi} (\mathrm{fast}\mathrm{neutron})+{\mathrm{C}}^{0}\ensuremath{\rightarrow}{\mathrm{C}}_{1}+\mathrm{vacancy},$ $(2) {\mathrm{C}}_{1}+{\mathrm{C}}_{1}\ensuremath{\rightarrow}{\mathrm{C}}_{2},$ $(3) {\mathrm{C}}_{1}+\mathrm{trap}\ensuremath{\rightarrow}{\mathrm{C}}_{1}T.$ Reaction (1) corresponds to the displacement of a single interstitial by collision of a fast (high-energy) neutron and the graphite lattice. This reaction is temperature independent. Reaction (2) represents the collision of two interstitials to form a stable ${\mathrm{C}}_{2}$ complex. The dimensional changes (rate of growth) occurring in graphite are due to the constant (zero-order) rate of formation of ${\mathrm{C}}_{2}$. Some of the single interstitials anneal (without causing dimensional changes) by being trapped at pores, edge atoms, etc. Reaction (3) describes this process. The rate-determining step for both reaction (2) and reaction (3) is the rate of migration of the single interstitial.