Sorting transition-metal diborides: New descriptor for mechanical properties

An enduring quest in materials research is to reconcile two of the most prominent yet often conflicting mechanical properties, hardness and toughness. Strong covalent solids like diamond exhibit superior hardness but are brittle, while ductile metals possess excellent toughness but are soft. Transition-metal (TM) carbides, nitrides, and borides offer a viable solution, where metal atoms provide the valence electrons to raise toughness and light elements form a covalent bonding network to build hardness. Among such compounds, TM diborides are especially promising for their optimal TM-boron ratios and boron's versatile bonding ability. Compared to carbides and nitrides, however, borides are less understood regarding key property trends and underlying mechanisms. Here, we report on a systematic first-principles study of a large series of group-IVB, VB and VIB dual-TM diborides in hexagonal structure to explore the brittle-ductile relation. Adopting the valence electron concentration (VEC) indicator previously used for the rocksalt structure nitrides, carbides and carbonitrides, we extend this approach to the description of mechanical properties of chemically and structurally different TM diborides, uncovering their notably superior structural stability and hardness and key mechanism. Most significantly, we identify the relative electronegativity (REN) of the constituent atoms in dual-TM diborides as a distinct indicator to regulate the widely scattered property trends under the VEC description. The composite VEC-REN descriptor constitutes a robust approach for accurately sorting mechanical properties by accounting for large data scatterings among compounds of the same VEC, thereby offering crucial insights into the mechanisms driving rich and well-regulated property trends in TM compounds. The strong and general physics and chemistry considerations for constructing the VEC-REN descriptor makes it a powerful and versatile tool, opening a new path for rational design and optimization of hardness-toughness balance in wide-ranging materials.