Features of the crystal structure of Tm$_{1-x}$Yb$_x$B$_{12}$ dodecaborides near a quantum critical point and at a metal-insulator transition

The magnetic phase diagram of Tm$_{1-x}$Yb$_x$B$_{12}$ antiferromagnets is determined from the specific heat measurements performed at low and ultralow temperatures ($0.07$–$10$ K). Precise experimental studies of the features of the crystal structure at room temperature suggest that a metal-insulator transition occurring in Tm$_{1-x}$Yb$_x$B$_{12}$ with the growth of $x$ is accompanied by a significant (by a factor of $2$–$6$) increase in the amplitude of atomic displacements in the boron and rare-earth sublattices. There is also a signature of an instability arising in the electron configuration of ytterbium ions at this transition. At room temperature, near the quantum critical point at $x_c\approx 0.25$, anomalies in the structural characteristics of dodecaborides under study are observed.