Geometrical frustration in an elemental solid: An Ising model to explain the defect structure of beta-rhombohedral boron

Recently, it was reported that beta-rhombohedral boron has a negative defect formation energy, which explains the presence of a macroscopic amount (4 at. %) of intrinsic defects. In this work, it is shown that the defects in boron have geometrical frustration described by an antiferromagnetic Ising model on an expanded kagome lattice, which is responsible for the reported macroscopic residual entropy. We suggest that the reported anomalies in the transport properties of beta-boron are due to the hopping of boron atoms between nearly degenerate configurations.