Fig. 1: Density functional theory studies describing the ductility.

The Poisson’s ratio (according to the Frantsevich’s criterion: ν > 0.26 for ductile materials⁶²) as a function of the G/B ratio (according to Pugh’s criterion, G/B > 0.571 for ductile materials⁶³) is indicated by orange pentagons. The G/B dependence of the Cauchy pressure over the polycrystalline Young’s modulus (CP/E > 0 for tough materials⁶⁴) is indicated with blue stars, gray triangles for literature data of cubic structures and blue circles for literature data of hexagonal structures. Our calculations are labeled using dotted–dashed lines. The ductile region is located at the left top corner (orange background), the brittle region at the bottom right corner (blue background). The dashed lines mark the various toughness criteria (the scale was chosen in a way that Frantsevich’s criterion and the criterion by Niu et al.⁶⁴ are on the same height). Exact values for literature data are given in Supplementary Table 1.