Evaluation of displacement damage in solids induced by fast positrons: Modeling and effect on vacancy measurement

Abstract

• The latest theoretical models of radiation damage in solid and numerical results of Mott differential cross section were used; • Displacement cross section by positrons for elements in most commonly used solids was calculated and the difference between positron and electron radiation was emphasized; • Displacement thresholds of kinetic energy for positrons in 30 elemental solids were presented; • Defects spatial distribution was obtained using Monte Carlo modeling. Positron Annihilation Technique is very sensitive to vacancy defects and small vacancy clusters and has been used as supplementary for TEM in radiation damage research. In this paper, we evaluated the displacement damage in solids induced by positrons and its effect on defects measurement, which has not been considered carefully in most PAT application. Displacement damage could only be produced when kinetic energy of positron exceeds a threshold determined by average displacement energy and the mass of atoms. Based on the latest models of displacement damage and numerical Mott elastic differential cross section of positrons interacting with atoms, displacement cross section for fast positron in solids was calculated and compared with that for electrons. In the energy range from 1 MeV to 100 MeV, electrons will produce more displacement defects than positrons do, especially in high-Z materials. Number of total defects depends on the primary displacement cross section and the size of damage cascades. To get distributions of defects and terminating position of positrons in materials, a Monte Carlo tool with full damage model was developed and validated. From the results of Monte Carlo modeling, the defects -generated by mono-energy positron beam have shallower distribution than the stopping position of positrons, indicating separation of defects and positrons and this fact benefits defects measurement because displacement damage produced by fast probing positron beam have little affection on the measurement. But for the positron beams from radioactive sources (such as 22 Na and 64 Cu) with continuous energy spectrum (from 0 to E max ), the depth profile of defects and terminated position of positrons overlap with each other and this fact indicated that defects measurement in materials will be affected by extra defects produced by positrons. The density of defects produced by positron beam is quite low with a typical value of about 0.01–0.1 cm −3 per positron in low-Z materials, which could be comparable with the defect density limitation if enough accumulated positrons are implanted into materials during measurement. For commonly used structural metals (such as Fe, Mn, Cu and metals with Z number higher than 40), using positron from 22 N and 64 Cu directly to measure defects density is quite safe because the energy is smaller than the displacement threshold.