Increase in specific heat and possible hindered rotation of interstitialC2molecules in neutron-irradiated graphite

Abstract

Irradiation-induced increase in the low-temperature specific heat has been measured in the temperature range of 1.9--43 K in graphite neutron-irradiated to $1.4\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }\text{n}/{\text{cm}}^{2}$ $(E>1\text{ }\text{MeV})$ around 333 K. The increase of the lattice specific heat is interpreted as due to the hindered rotation of interstitial ${\text{C}}_{2}$ molecules in the periodic potential of $V(\ensuremath{\varphi})=({V}_{0}/2)(1+\text{cos}\text{ }2\ensuremath{\varphi})$, where $\ensuremath{\varphi}$ is the angle of rotation and ${V}_{0}$ is 0.040 eV. The first-excited rotational level is 0.0058 eV above the ground state and the rotational frequency is $1.39\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }{\text{s}}^{\ensuremath{-}1}$. This result shows that ${\text{C}}_{2}$ molecules do not form covalent bonds with atoms in the surrounding graphite layers. It is in marked contrast with the result of recent first-principles theoretical calculations that interstitial atoms form strong covalent bonds with atoms in the graphite layers. The concentration of ${\text{C}}_{2}$ molecules is estimated to be $f=1.16%$. The hole concentration, deduced from the electronic specific heat and the SWMcC band model, suggests that one single vacancy creates one hole and the single vacancy concentration is $2f$. Since the measurement of the lattice specific heat gave the concentration of the defects directly, we could evaluate some physical properties for a unit concentration of the defects. The volume changes by a single interstitial atom, an interstitial ${\text{C}}_{2}$ molecule, and a single vacancy are deduced to be $2.6\ifmmode\pm\else\textpm\fi{}0.3$, $9.3\ifmmode\pm\else\textpm\fi{}1.4$, and $\ensuremath{-}0.46\ifmmode\pm\else\textpm\fi{}0.07$ atomic volumes, respectively. The formation energy of a Frenkel pair is estimated to be $12.6\ifmmode\pm\else\textpm\fi{}2.5\text{ }\text{eV}$. The phonon scattering with a reciprocal relaxation time proportional to ${\ensuremath{\omega}}^{1.5}$, where $\ensuremath{\omega}$ is the angular frequency of phonons, is attributed to the scattering of phonons by the disklike strain around interstitial ${\text{C}}_{2}$ molecule clusters. A broad dip in the $a$-axis thermal conductivity observed below room temperature is attributed to the resonance scattering of phonons by the hindered rotation of interstitial ${\text{C}}_{2}$ molecules as well as by the vibration of these molecules as rigid units. The positron lifetime of 350 ps is suggested to be the lifetime of positrons trapped in an open space on the periphery of the interstitial clusters of ${\text{C}}_{2}$ molecules. The well-known Wigner energy is stored mainly as interstitial ${\text{C}}_{2}$ molecules and single vacancies.