Disordering of Solids by Neutron Radiation

A general method is outlined for determining the number of vacant lattice sites or interstitial atoms in a monatomic solid exposed to neutron radiation. The colliding atoms are assumed to be within the energy range for which the orbital picture can be applied. Following the treatment of Bohr, the scattering regions of excessive and moderate screening, Rutherford distribution, and electronic collisions are considered separately. The number of vacancies or interstitial atoms as a function of the energy of the primary knocked-out atom is given by the solution of certain integral equations that are different for various energy regions considered. It is found that if the velocity of a recoil atom resulting from neutron collision is less than $\frac{e^2}{\hslash }$ (region of elastic collisions) approximately half of its energy is used up to produce vacancies or interstitials. If the velocity of the recoil atom is above $\frac{e^2}{\hslash }$ (region of inelastic collisions) then the energy used up to produce vacancies and interstitials is approximately constant for medium and heavy elements. A simple formula has been derived expressing the average number of vacant lattice sites or interstitials produced in a collision of a neutron having energy $E$ in a monatomic solid composed of medium or heavy elements having atomic mass $M$. The formula is as follows: $G\left(E\right)\mathrm{}\sim \frac{{(nE-\alpha )}^2}{4\alpha \mathrm{nE}} \mathrm{for} E\leqq \frac{\gamma }{n},$ $G\left(E\right)\mathrm{}\sim \frac{[{(nE-\alpha )}^2-(1-\overline{R}\left){(nE-\alpha -\gamma )}^2\right]}{4\alpha \mathrm{nE}} \mathrm{for} E\geqq \frac{\gamma }{n},$ where $\gamma =\frac{M{e}^4}{2{\hslash }^2}$; $n=\frac{4M}{{\mathrm{}(M+1\mathrm{})\mathrm{}}^2}$, $\alpha$ is the binding energy of an atom in the lattice, and $\overline{R}$ is a slowly varying function of $Z$.