Theory of light interstitials in bcc metals. I. Self-trapped state of hydrogen and muons in Nb

Abstract

A quantum-mechanical calculation has been performed on the self-trapped state of hydrogen isotopes and positive muons in Nb. By solving a Schr\"odinger equation for these light interstitials in the field of interaction with surrounding metal atoms, the energy and the wave function of the interstitials and the displacements of metal atoms have been derived. It is concluded, in particular, that hydrogen isotopes occupy tetrahedral ($T$) sites, and positive muons occupy octahedral ($O$) sites in Nb. The origin of the systematic variation of the relative stability of $O$ sites vs $T$ sites is clarified. Some calculations performed on the excited state are also described.