Section 4.1.5.2. Positrons and muons

These elementary particles are used in crystallography mainly in studies of lattice defects (vacancies, interstitials, and impurity atoms) for the determination of their concentration, location, and diffusion by means of the techniques such as positron annihilation spectroscopy (PAS) and muon spin resonance (μSR) – see, for example, Siegel (1980) and Gyax, Kündig & Meier (1979). The positron implantation range in a solid is  100 μm from the positron sources usually used (e.g. ²²Na, ⁶⁴Cu, ⁵⁸Co); these sources yield positrons with end-point energies of 1 MeV. The PAS techniques are based on lifetime, Doppler broadening or angular correlation measurements of γ-rays emitted by the decaying nucleus of the radioactive source and those resulting from the positron–electron annihilation process. Muon sources require intense primary medium-energy proton beams. The positive muon μ⁺ has charge +e, spin 1/2, mass 105.659 MeV/c² and a magnetic moment equal to 1.001 of the muon–magneton units. With a mean lifetime of 2.197 μs, the muon decays into a positron (e⁺) and two neutrinos and ). The correlation between the direction of the emitted positron and the spin direction of the muon allows one to measure the spin precession frequency and/or the decay of the muon polarization of an ensemble of muons implanted in a solid.