Cohesive energy, phonon spectra, and thermodynamic properties of elements with the structures A1, A2, A3, A4—Al, Cu, V, Ti, Mg, Si, and Sn

The dependences of the cohesive (atomization) energy on the interatomic distance for elements Al, Cu, Ti(A2), V, Mg, Ti(A3), Si, and Sn are calculated using methods based on the Thomas-Fermi-Dirac-Gambosh statistical atomic theory. The obtained dependences are approximated by the Mie-Gruneisen potential. The phonon spectra calculated on the basis of the Born-Karman model and the Born-Karman-Blackman-de Lunay approach are used to determine the temperature dependences of the specific heat, free energy, and internal energy of the elements under investigation. The calculated cohesive energy, equilibrium interatomic distances, and temperature dependences of the specific heat agree with the experimental data.