Symmetry lowering under high pressure: Structural evidence for $f$-shell delocalization in heavy rare earth metal terbium

Heavy rare earth metal terbium has been studied at synchrotron sources using both angular and energy dispersive x-ray diffraction to a maximum pressure of $155\mathrm{GPa}$ (volume fraction $V∕V_0=0.39$). The complete regular trivalent rare earth structural sequence, $\mathrm{hcp}\to \alpha \text{−}\mathrm{Sm}\to \text{double}$ $\mathrm{hcp}\to \mathrm{fcc}\to \text{distorted}$ fcc $\left(hR24\right)$, is observed at low pressures except for the undistorted fcc. At $51\pm 2\mathrm{GPa}$, terbium undergoes a 5% volume collapse transitioning to $C2∕m$ monoclinic. The open, low symmetry structure is reminiscent of the $4f$ delocalization phenomenon in the light rare earth metals, particularly the ${\alpha }^{″}$ phase of cerium.

Figure 1

Angle dispersive x-ray diffraction (ADXD) spectrum of terbium showing the $hR24$ distorted-fcc phase at $40.2\mathrm{GPa}$. Sample peaks are labeled by their fitted $hkl$ values, and reflections from the copper pressure marker are marked with an asterisk. This $hR24$ phase is similar to the one proposed by Hamaya et al. (1994) for light rare earth metal praseodymium, and is the first phase in terbium, which cannot be explained by pressure-induced occupation of the $d$ band. The x-ray wavelength $\lambda =0.3678$ and sample-detector distance is $350\mathrm{mm}$.

Figure 2

ADXD spectrum of terbium at the highest pressure of $155\mathrm{GPa}$ in the $C2∕m$ phase. Sample peaks are labeled by their fitted $hkl$ values, and reflections from the copper pressure marker are marked with an asterisk. The $C2∕m$ phase is similar to the ${\alpha }^{″}$ monoclinic phase observed in cerium and is taken as evidence in favor of delocalization of the $f$-shell electrons. The x-ray wavelength $\lambda =0.3678$ and sample-detector distance is $350\mathrm{mm}$.

Figure 3

Volume per atom as a function of pressure; filled symbols are decompression data points. The equation of state has been measured to $155\mathrm{GPa}$ at room temperature and includes data points from both experiments I and II. The complete regular trivalent rare earth structural sequence is observed with the exception of fcc, which was not observed as a pure phase. At $51\pm 2\mathrm{GPa}$, a 5% volume collapse is observed as the structure transitions to the open, low symmetry $C2∕m$ phase. Note the sharp decrease in compressibility for this phase, indicating a change in the character of the metallic bonds, which is argued to be the onset of $f$-electron participation in bonding.