Influence of a Variable Ejection Probability on the Displacement of Atoms

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Abstract
A model for the displacement of atoms is used in which each atom of a crystal has a threshold energy that is a random variable. Three quantities are derived as a function of the probability density of this random variable. First the total number of displaced lattice atoms resulting from an initial energetic atom is found as a function of the kinetic energy of the moving atom. Second, the average number of displaced lattice atoms per atom initially displaced by external radiation is derived. Third, the total number of displaced atoms resulting from a given dose of radiation is determined. Both charged particle and neutron radiation are considered. It is shown that the shapes of all these quantities, for moderately large energies of the bombarding particles, are independent of the nature of the probability density governing the displacement energy; the probability density determines only an amplitude factor. It is shown further that the physical effects of bombardment by either neutrons or charged particles can be pictured as arising from an "effective sharp-threshold energy" determined by the probability density functions and that this effective threshold is the same for both types of bombardment. Finally, it is shown that, if the present factor of about five between the theory of radiation damage and the corresponding experiments is to be explained solely on the basis of a variable probability of ejection, a considerable fraction of the atoms in a solid must have a surprisingly large threshold energy.

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