# An unconventional mechanism for simultaneous high hardness and ductility in Mo$_2$BC

## TL;DR

This study reveals the atomic-level mechanism behind Mo$_2$BC's unique combination of high hardness and ductility, showing how electronic structure changes under strain contribute to its exceptional mechanical properties.

## Contribution

It uncovers the strain-induced electronic and structural changes responsible for Mo$_2$BC's simultaneous hardness and ductility, a phenomenon rarely observed in crystalline materials.

## Key findings

- Mo$_2$BC exhibits anisotropic stress response and strain-stiffening behavior.
- Formation of a pseudogap and boron-boron dimerization under strain enhances covalent bonds.
- The material delays failure through electronic metastability under extreme strain.

## Abstract

Materials either have a high hardness or excellent ductility, but rarely both at the same time. Mo$_2$BC is one of the only crystalline materials that simultaneously has a high Vickers hardness and is also relatively ductile. The origin of this unique balance between hardness and ductility is revealed herein using first-principles stress-strain calculations. The results show an anisotropic response including a remarkable intermediate tensile strain-stiffening behavior and a two-step sequential failure under shear strain. The mechanism governing the mechanical properties more closely resembles ductile soft materials like biological systems or some polymer networks rather than hard, refractory metals. This unforeseen response is established by analyzing changes in the electronic structure and the chemical bonding environments under mechanical perturbation. Most importantly, the optimized structure under extreme strain shows the formation of a pseudogap in the density of states and dimerization of the structure's boron-boron zigzag chain. This leads to an enhancement of these strong covalent bonds that help delay the ultimate failure until higher than the anticipated strain. These results provide a platform for developing a new generation of high hardness, ductile materials by identifying compounds that form electronically metastable structures under extreme strain.