Diffusion of a probe nanoparticle in a quantum crystal with narrow vacancy band

Abstract

The vacancy-assisted diffusion of a probe nanoparticle with a diameter d_p of a few nm drifting through a quantum crystal with a narrow vacancy band Q_v << T_melt is considered qualitatively. Below the melting point T_melt the temperature dependence of the diffusion coefficient of the nanoprobe, D_p(T), changes significantly at temperatures near T_tr (T_melt≥T_tr≥Q_v), where the transition from thermally activated hopping of localized vacancies to a proper band motion of delocalized vacancions takes place. Moreover, if the mean free path of the vacancions l_v(T) at T_tr is less than d_p and increases with lowering temperature quicker than x_v^-1 (here x_v is the relative concentration of the thermal vacancies) the diffusion coefficient D_p of the nanoprobe drifting in the dense gas of quasiparticles grows with cooling the sample. At T << T_tr, in the rarified gas of quasiparticles where l_v >> d_p, the diffusion coefficient D_p falls almost near exponentially, proportionally with x_v, if the cross-section of inelastic vacancion-probe particle scattering is weakly dependent on temperature. We believe that our model could be applied for the description of the diffusion of positive charges in hcp ⁴He crystals grown at pressures higher than the minimal pressure of helium solidification and the diffusion of negative charges in hcp crystals grown from pure parahydrogen.