Icosahedral superstrength at the nanoscale

Materials that exhibit extreme hardness, low mass density, and high thermal/chemical stability can often be modeled as simple modifications to the $\ensuremath{\alpha}$-rhombohedral phase of boron. To facilitate the development and discovery of these multipurpose, structural ceramics, the current work reveals fundamental physics on the bonding and deformation of $p$-block hexaborides, an important and representative subclass of icosahedral solids. Icosahedral separation and localization of equatorial bonding are identified as predictors of both elastic moduli and strength. This work also explores nanotwinning, an advanced nanostructure responsible for dramatic records in mechanical performance of both metals and ceramics. To help develop the first model of nanotwinning in ceramics, this work demonstrates (1) that susceptibility to nanotwinning relies on key bonding traits and (2) that nanotwinning minimally affects elasticity and high-periodicity inelasticity. Overall, this work helps rationalize both the mechanical performance of a major class of materials and the cutting-edge mechanism of nanotwinning through fundamental, physics-based approaches.