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.

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.

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