Light hydrogen isotopeμ+in Sc andα−ScHxsolid solutions

Abstract

The response of Sc and $\ensuremath{\alpha}\ensuremath{-}{\mathrm{ScH}}_{x}$ systems $(0<~x<~0.25)$ to the implantation of positive muons, i.e., light H isotopes, has been studied by ${\ensuremath{\mu}}^{+}\mathrm{SR}$ spectroscopy in high and low transverse magnetic field, and in zero field (ZF). The investigation covered a temperature range from 300 K down to 2 K, for various orientations of the single-crystal samples with respect to the field or initial ${\ensuremath{\mu}}^{+}$ polarization. Below 30 K the positive muons occupy, in pure Sc, a localized ``fast-tunneling'' state, extending over two adjacent, interstitial-tetrahedral (T) sites above and below the $\mathrm{ab}$-atomic plane of the hcp lattice. In $\ensuremath{\alpha}\ensuremath{-}{\mathrm{ScH}}_{x},$ a fraction of the muons stays in this tunneling state, while for the other part, the muons pair with a H atom, to form the analog of the T-pair state H-Sc-H aligned along the c axis, specific to the ${\ensuremath{\alpha}}^{*}$ phase. The electric-field gradients, of muonic as well as intrinsic-crystalline origin, acting on the nuclei near the ${\ensuremath{\mu}}^{+}$ influence the results at low and zero magnetic fields. Their characteristics and the H-concentration dependences are evaluated. For the ZF-data analysis a newly developed uniaxial version of the Kubo-Toyabe formula was applied. Above 30 K the long-range diffusion of positive muons becomes noticeable; a two-state model explains very well the data. It assumes the ${\ensuremath{\mu}}^{+}$ to be, alternatively, in a state of free diffusion between localized-tunneling states or in a ${\ensuremath{\mu}}^{+}$-Sc-H trap. The model describes the repeated ${\ensuremath{\mu}}^{+}$-capture and release processes with three characteristic correlation times, which follow Arrhenius laws. The parameters, e.g., activation energies and preexponential factors, are compared to the parameters of the H and D dynamics in $\ensuremath{\alpha}\ensuremath{-}\mathrm{ScH}{(D)}_{x}.$ From $\ensuremath{\mu}\mathrm{SR}$ measurements in a deuterated sample $(\ensuremath{\alpha}\ensuremath{-}{\mathrm{ScD}}_{0.10})$ one infers very similar behaviors of the ${\ensuremath{\mu}}^{+}$ in D and H solid solutions in the Sc host.