Figure 2

Extra-electron induced covalent strengthening.

(a)-(d), Total DFT electronic densities of states of FCC-Al, Al₁₂W-type Al₁₂X (X = Re, □ and He). □ denotes that X is replaced by a vacancy. Here, Al₁₂□ and Al₁₂He are artificial and unstable, as evidenced by their positive enthalpies of formation (Supplementary Table S1). Their DOS profiles are compared with those obtained using the classic free electron model. e and f, Section contour maps of the difference of charge densities for e the Al-Al covalent bonds connecting the nearest-neighboring icosahedra as illustrated by the (020) plane and f the intra Al-Re covalent bonds within the Al₁₂ icosahedron in the (0y0) plane of Al₁₂Re. Similar results have been observed for all other Al₁₂X (X = Cr, Mo, W, Mn and Tc), but are not shown here. The red and blue isovalues correspond to the charge accumulations and depletions, respectively. g, The comparison of calculated bulk moduli (B in GPa), Young moduli (E in GPa), shear moduli (G in GPa) and Cauchy pressure C₁₂-C₄₄ as well as Pugh'smodulus ratio of G/B (right side) in the series of Al₁₂□, FCC Al and Al₁₂X (X = Cr, Mo, W, Mn, Tc and Re) (details refer to Supplementary Table S3 which summarizes all elastic data used here).