Vacancies and Displacements in a Solid Resulting from Heavy Corpuscular Radiation

Abstract

The number of displacements $D(E)$ and the number of vacancies $V(E)$ produced in a monatomic solid as a result of collisions due to an incident ion of initial energy $E$, are obtained as solutions of the equation $f(E)=\ensuremath{\int}{0}^{E}dyK(E, y){p(y)[f(y\ensuremath{-}\ensuremath{\alpha})+1\ensuremath{-}\ensuremath{\theta}q(E\ensuremath{-}y)]+[1\ensuremath{-}p(E\ensuremath{-}y)q(y)]f(y)},$ where $f(E)=D(E) or V(E), p(y)$ denotes the probability that a struck atom is displaced when it has received energy $y$, $q(E\ensuremath{-}y)$ is the probability that the striking atom replaces it if displacement has occurred, $K(E, y)$ is the scattering kernel, and $\ensuremath{\alpha}$ is the minimum amount of energy that is assumed to be necessary to displace an atom (it is assumed that the struck atom loses energy $\ensuremath{\alpha}$ in breaking away from its lattice site). In the equation, $f(E)=0$ for $E<\ensuremath{\alpha}$, with $\ensuremath{\theta}=0$ for displacements and $\ensuremath{\theta}=1$ for vacancies.This equation is solved for some representative cases of $p(y)$ and $q(y)$. The functions $p(y)$ and $q(y)$ can be chosen to fit experimental estimates of either $D(E)$ or $V(E)$ singly but indicate a fundamental discrepancy of the joint estimates. The discrepancy, if not due to inaccuracy in the interpretation of experimental results, suggests that a mathematical model based on individual collisions is inadequate.