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

The temperature dependence of the diffusion coefficient Dp(T) of a probe particle with a diameter dp of several nanometers and moving in a quantum crystal with a narrow vacancy band Qv≪Tmelt changes substantially, as a result of interactions with thermal vacancies, with decreasing temperature in the range Tmelt⩾Ttr⩾Qv, where a transition occurs from classical thermally activated vacancy hopping to coherent motion of delocalized vacancies. Moreover, in the transitional range T≈Ttr the diffusion coefficient of a probe particle in a viscous vacancion gas can increase if the effective vacancion mean-free path length is small compared to the particle diameter lv≪dp and increases with decreasing temperature more rapidly than the concentration of thermal vacancies xv∼exp(−Ev/T). For T≪Ttr, in a rarefied vacancion gas where lv≫dp the particle diffusion coefficient Dp(T)∼xvSvp decreases as xv if the cross section Svp for the inelastic scattering of a vacancion by a probe particle is a weak function of the temperat...