Mechanical and thermodynamical properties of hexagonal compounds at optimized lattice parameters from two-dimensional search of the equation of state
We have calculated the mechanical and thermodynamical properties of selected hexagonal structures by using the optimized lattice parameters (a and c) from two-dimensional (2D) search of the equation of state (EOS) within the appropriate exchange–correlation functional. To overcome the deficiency of density functional theory (DFT) for compounds with localized electrons, a PBE + U approximation was used with our calculated effective U parameter. For calculating the elastic constants of hexagonal structure, the Hex-elastic package was used which is compatible with the highly accurate all electron full-potential (Linearized) augmented plane-wave plus local orbital [FP-(L)APW + lo] method as implemented in the WIEN2k code. The obtained results of the 2D-search of the EOS for the optimized lattice parameters (a and c) are in good agreement with the experimental data. This method clearly shows its superiority compared to the 1D-search of the EOS method. Furthermore, the obtained elastic constants by using the optimized lattice parameters (a and c) from the 2D-search, were in good agreement with the available experimental data and better than the previous theoretical calculations. Our calculations show that the PBE + U approximation improves the results for elastic constants. Consequently, we can claim the following predictions; first, we suggest the value of Poisson's ratio as a boundary condition to predict the type of bonds. Second, we make a one-to-one correspondence between two quantities, shear modulus and C55. Third, we predict the stiffness of the material from the Debye temperature and average sound velocity.