Crystal structures of dodecaborides: complexity in simplicity

Abstract

Analysis of the intriguing physical properties of the dodecaborides, $R$B${}_{12}$, requires accurate data on their crystal structure. We show that a simple cubic model fits well with the atomic positions in the unit cell but cannot explain the observed anisotropy in the physical properties. The cooperative Jahn-Teller (JT) effect slightly violates the ideal metric of the cubic lattice and the symmetry of the electron density distribution in the lattice interstices. Theoretical models of the JT distortions of the boron framework are presented. Their correspondence to the electron-density distribution on the maps of Fourier syntheses obtained using x-ray data and explaining the previously observed anisotropy of conductive properties is demonstrated. The effect of boron isotope composition on the character of the lattice distortions is shown. We also discuss the application of the Einstein model for cations and the Debye model for the boron atoms to describe the dynamics of the crystal lattice.

arXiv commentChapter 3 of the review volume "Rare-Earth Borides", edited by Dmytro S. Inosov, to be published by Jenny Stanford Publishing (2021), ISBN 978-9814877565

References in corpus (1)

• The lower symmetry electron-density distribution and the charge transport anisotropy in cubic dodecaboride LuB12

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• Novel Magnetoacoustic Resonance Technique for Exploring Hidden Quadrupoles in a Crystal Field Quartet