Figure 4 | Scientific Reports

Figure 4

From: Ceramic transition metal diboride superlattices with improved ductility and fracture toughness screened by ab initio calculations

Figure 4

Ductility map for mechanically stable \(\alpha\)/\(\alpha\) (a, b) and \(\alpha\)/\(\omega\) (c, d) diboride SLs satisfying our stability, lattice and shear modulus mismatch criteria. The Cauchy pressure, \(CP_{\parallel }=C_{12}-C_{66}\) (in-plane) and \(CP_\perp =C_{13}-C_{44}\) (out-of-plane), is plotted against the shear-to-bulk modulus ratio (G/B). Dashed lines guide the eye for Pettifor’s43 and Pugh’s44 ductility criteria, while the symbol size and colour is based on the average valence electron concentration (VEC) of the M elements. Mind different y-axis ranges for (a, b) vs. (c, d).

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