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Based on the first principles calculation combined with quasi-harmonic approximation, in this work we focus on the analysis of temperature dependent lattice geometries, thermal expansion coefficients, elastic constants and ultimate strength of graphene and graphyne. For the linear thermal expansion coefficient, both graphene and graphyne show a negative region in the low temperature regime. This coefficient increases up to be positive at high temperatures. Graphene has superior mechanical properties, with Young modulus E 11 =371.0 N/m, E 22 =378.2 N/m and ultimate tensile strength of 119.2 GPa at room temperature. Based on our analysis, it is found that graphene's mechanical properties have strong resistance against temperature increase up to 1200 K. Graphyne also shows good mechanical properties, with Young modulus E 11 =224.7 N/m, E 22 =223.9 N/m and ultimate tensile strength of 81.2 GPa at room temperature, but graphyne's mechanical properties have a weaker resistance with respect to the increase of temperature than that of graphene.

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The unsteady viscous flow over a continuously shrinking surface with mass suction is studied. The solution is fortunately an exact solution of the unsteady Navier-Stokes equations. Similarity equations are obtained through the application of similarity transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the mass suction parameters and the unsteadiness parameters. Results show that multiple solutions exist for a certain range of mass suction and unsteadiness parameters. Quite different flow behaviour is observed for an unsteady shrinking sheet from an unsteady stretching sheet.

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Under a static high magnetic field of 10 T, diamond-like carbon (DLC) nanocrystals and graphite-coated n-diamond nanoparticles have been synthesized after a pyrogenation of carbon black and a nanometre-sized iron catalyst at atmospheric pressure and a temperature of 1100 °C. The product is analysed by x-ray diffraction, Raman spectroscopy, transmission electron microscopy and electron-probe microanalysis. The average size of the DLC nanopowders is about 20 nm, and that of the graphite-coated n-diamond particles is about 100 nm. The yield of diamond is as high as 30%.

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To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at given temperature and pressure was derived, hence the full minimization of the Gibbs free energy with respect to temperature and lattice parameters can be put into effective operation by using first principles. Therefore, with this new theory, anisotropic thermal expansion and temperature dependent elastic constants can be obtained for crystals with arbitrary symmetry. In addition, we apply our method to hexagonal beryllium, hexagonal diamond and cubic diamond to illustrate its general applicability.