Features of the local structure of rare-earth dodecaborides $\mathrm{RB}_{12}$ ($\mathrm{R} = \mathrm{Ho}, \mathrm{Er}, \mathrm{Tm}, \mathrm{Yb}, \mathrm{Lu}$)

The parameters of the local crystal structure of dodecaborides $\mathrm{RB}_{12}$ ($\mathrm{R} = \mathrm{Ho}, \mathrm{Er}, \mathrm{Tm}, \mathrm{Yb}, \mathrm{Lu}$) have been determined by extended X-ray absorption fine structure (EXAFS) spectroscopy. It has been shown that the vibrations of the rare-earth ion with respect to the boron cage are well described in the harmonic approximation. At the same time, the displacement of rare-earth ions from equilibrium positions of the crystal structure should be taken into account to determine the length of the $\mathrm{R}$–$\mathrm{B}$ bond. The analysis of EXAFS spectra has revealed the displacement of $1$–$6\%$ of rare-earth ions by about $0.2$–$0.3$ Åin all compounds under investigation; this displacement at low temperatures results in the formation of a cage glass phase.