Figure 1

(Color) DFT calculation results of 22 materials (metallic: blue, ionic: green, covalent: red). (a) Relaxed, and (b) unrelaxed ideal shear stresses (normalized) and shear strains. The solid line indicates a unit slope, while the dashed line corresponds to a slope of $2∕\pi$. The ionic solids are far out of range in (b) and are shown in the inset.Reuse & Permissions

Figure 2

(Color) Valence charge density $\rho \left(\mathbf{x}\right)$ isosurface plots of (a) $\mathrm{FCC}\mathrm{Ag}$, (b) $\mathrm{FCC}\mathrm{Al}$, (c) $\mathrm{BCC}\mathrm{Mo}$, (d) diamond cubic $\mathrm{Si}$, at their stress-free states. ${\Omega }_0$ is the atomic volume.Reuse & Permissions

Figure 3

(Color) Relaxed shear stress-strain curves of 22 materials, rescaled such that all have unit slope initially and reach maximum at 1. The renormalized Frenkel model Eq. (1) is shown for comparison.Reuse & Permissions

Figure 4

(Color) Ideal tensile strengths and tensibilities (volumetric) of 22 materials. Note the narrower range of data compared to Fig. 1.Reuse & Permissions

Figure 5

(Color) Schematic map of material ideal strengths, showing stability boundaries (dashed curves) of the affine strain energy landscapes for metals and ceramics, beyond which bonds break spontaneously in a perfect crystal (Ref. 34). $s_m$ and $t_m$ indicate the maximum stable engineering shear and volumetric tensile strains of a perfect crystal, respectively. Ceramics tend to have larger shearability $s_m$ than metals, with $s_m$ depending not only on the crystal structure (reference value is $b∕4d_0$), but also on the nature of bonding (e.g., 0.105 in $\mathrm{FCC}\mathrm{Au}$ vs 0.200 in $\mathrm{FCC}\mathrm{Al}$), and the loading condition (e.g., 0.221 in relaxed vs 0.658 in unrelaxed shear, in $\mathrm{NaCl}$). In contrast, the relative variation of tensibility $t_m$ of solids in more limited ($0.38–0.67$ in the 22 materials studied). As in the Universal Binding Energy Relation (UBER) (Ref. 2) for tension, a two-parameter model for shear can be established by modifying the empirical formula of Frenkel (Ref. 1). Based on Figs. 1, 3, 4 and elastic moduli for shear and tension, a simple scaling relation Eq. (2) suggests it is much more difficult to break bonds in ceramic solids in shear than in metals, relative to in tension. Electronic-structure features such as valence charge localization and anisotropy are found to correlate strongly with mechanical-response features during deformation [see Fig. 2 and Supplementary Material (Ref. 22)], such as the shearability.Reuse & Permissions