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Molecular dynamics simulations with adaptive intermolecular reactive empirical bond order (AIREBO) potential are performed to investigate the effects of rectangular nanoholes with different areas, aspect ratios (length/width ratios) and orientations on the tensile strength of defective graphene. The simulations reveal that variation of area, aspect ratio and orientation of rectangular nanohole can significantly affect the tensile strength of defective graphene. For example, defective graphene with a larger area of rectangular nanohole shows a bigger drop in tensile strength. It was found that the tensile strength of both armchair and zigzag edged graphene monotonically decreases with area increases in rectangular nanohole. Changes in aspect ratio and orientation of rectangular nanohole, however, can either decrease or increase the tensile strength of defective graphene, dependent on the tensile direction. This study also presents information that the tensile strength of defective graphene with large area of nanohole is more sensitive to changes in aspect ratio and orientation than is defective graphene with small area of nanohole. Interestingly, variation of tensile strength of defective graphene from MD simulations is in good agreement with predictions from energy-based quantized fracture mechanics (QFM). The present results suggest that the effect of nanoholes on the tensile strength of graphene provides essential information for predictive optimization of mechanical properties and controllable structural modification of graphene through defect engineering.

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The effects of doping on the electronic and magnetic properties of the quaternary Heusler alloy TiZrCoIn were investigated by first-principles calculations. Results showed that the appearance of half-metallicity and negative formation energies are associated in all of the TiZrCoIn1−xGex compounds, indicating that Ge doping at Z-site increases the stability without damaging the half-metallicity of the compounds. Formation energy gradually decreased with doping concentration, and the width of the spin-down gap increased with a change in Fermi level. TiZrCoIn0.25Ge0.75 was found to be the most stable half-metal. Its Fermi level was in the middle of the broadened gap, and a peak at the Fermi level was detected in the spin majority channel of the compound. The large gaps of the compounds were primarily dominated by the intense d-d hybridization between Ti, Zr, and Co. The substitution of In by Ge increased the number of sp valence electrons in the system and thereby enhanced RKKY exchange interaction and increased splitting. Moreover, the total spin magnetic moments of the doped compounds followed the Slater–Pauling rule of Mt = Zt − 18 and increased from 2 μB to 3 μB linearly with concentration.

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