Diffusion of positive muons and other light particles in metals

Abstract

The paper gives a survey of the principal techniques available for the experimental determination of the diffusivityD ^μ+(T) of positive muons in crystals (Gurevich technique, trapping, longitudinal muon-spin relaxation, transverse muon-spin relaxation in superconductors) and discusses their strengths and weaknesses. The main theoretical ideas of the quantum theory of diffusion are outlined and the distinction between different mechanisms is emphasized. It is argued that at high temperaturesT the so-called adiabatic regime with a preexponential factor of the diffusivity of the order of magnitudeΝ _D d ² (Ν _D = Debye frequency of the host crystal,d=“jump” distance of the muons) always exists. In the fcc metals and in the case of¹H in Nb it is followed by a so-called Flynn-Stoneham regime at intermediate temperatures, whereas forμ ⁺ in Nb andα-Fe such a regime is not observed. Instead, in these cases the adiabatic regime appears to go over directly to the few-phonon regime of incoherent tunnelling between adjacent ground states, leading to the one-phononD ^μ+ ~T law at low temperatures.

The metal best-studied with regard to muon diffusion,α-Fe, is used to illustrate the theoretical analysis of experimental results in some detail. In an Appendix the theoretical expressions required for the quantitative determination ofD ^μ+ by the Gurevich technique are collected.