Crystal structures of dodecaborides: complexity in simplicity

TL;DR

This paper investigates the crystal structure of $R$B$_{12}$ dodecaborides, revealing how Jahn-Teller effects and isotope variations influence their anisotropic physical properties through detailed structural and theoretical analysis.

Contribution

It provides a comprehensive analysis of the crystal structure and Jahn-Teller distortions in dodecaborides, linking structural features to anisotropic properties and isotope effects.

Findings

Simple cubic model fits atomic positions

Jahn-Teller effect causes lattice symmetry violations

Isotope composition affects lattice distortions

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.