Plenty of new two-dimensional materials including graphyne, graphdiyne, graphone, and graphane have been proposed and unveiled after the discovery of the "wonder material" graphene. Graphyne and graphdiyne are two-dimensional carbon allotropes of graphene with honeycomb structures. Graphone and graphane are hydrogenated derivatives of graphene. The advanced and unique properties of these new materials make them highly promising for applications in next generation nanoelectronics. Here, we briefly review their properties, including structural, mechanical, physical, and chemical properties, as well as their synthesis and applications in nanotechnology. Graphyne is better than graphene in directional electronic properties and charge carriers. With a band gap and magnetism, graphone and graphane show important applications in nanoelectronics and spintronics. Because these materials are close to graphene and will play important roles in carbon-based electronic devices, they deserve further, careful, and thorough studies for nanotechnology applications.

The structural and mechanical properties of graphene-like honeycomb monolayer structures of MoS₂ (g-MoS₂) under various large strains are investigated using density functional theory (DFT). g-MoS₂ is mechanically stable and can sustain extra large strains: the ultimate strains are 0.24, 0.37, and 0.26 for armchair, zigzag, and biaxial deformation, respectively. The in-plane stiffness is as high as 120 N m⁻¹ (184 GPa equivalently). The third, fourth, and fifth order elastic constants are indispensable for accurate modeling of the mechanical properties under strains larger than 0.04, 0.07, and 0.13 respectively. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson ratio monotonically decreases with increasing pressure. With the prominent mechanical properties including large ultimate strains and in-plane stiffness, g-MoS₂ is a promising candidate of elastic energy storage for clean energy. It possesses a theoretical energy storage capacity as high as 8.8 MJ L⁻¹ and 1.7 MJ kg⁻¹, or 476 W h kg⁻¹, larger than a Li-ion battery and is environmentally friendly.

We investigated the mechanical properties of graphyne monolayers using first-principles calculations based on the Density Functional Theory. Graphyne has a relatively low in-plane Young's modulus (162 N m⁻¹) and a large Poisson ratio (0.429) compared to graphene. It can sustain large nonlinear elastic deformations up to an ultimate strain of 0.2 followed by strain softening until failure. The single bond is more vulnerable to rupture than the triple bond and aromatic bond, although it has a shorter bond length (0.19 Å shorter) than the aromatic bond. A rigorous continuum description of the elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the fifth-order term. We obtained a total of fourteen nonzero independent elastic constants which are components of tensors up to the tenth order. Pressure effects on the second-order elastic constants, in-plane Young's modulus, and Poisson ratio are predicted. This study implies that graphyne-based surface acoustic wave sensors and waveguides may be synthesized by introducing precisely controlled local strains on graphyne monolayers.

The mechanical stabilities of planar (g) and low-buckled (b) honeycomb monolayer structures of silicon under various large strains are investigated using density functional theory (DFT). The mechanical properties, including the ultimate stresses, ultimate strains, and high order elastic constants of silicene are predicted, as well as the structure evolutions. Both g-Si and b-Si can sustain large strains (η ≥ 0.15) for armchair, zigzag, and biaxial deformation. The third, fourth, and fifth order elastic constants are indispensable for accurate modeling of the mechanical properties under strains larger than 0.03, 0.06, and 0.08 respectively. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson ratio monotonically decreases with increasing pressure. Our results on the positive ultimate strengths and strains, second order elastic constants, and the in-plane Young's modulus indicate that both g-Si and b-Si are mechanically stable.

Three density functional approximations (DFAs), PBE, PBE+U, and Heyd–Scuseria–Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe₂O₃, Fe₃O₄, and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% “screened” Hartree–Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.