A study was carried out of the reciprocal lattice of metal crystals with cells I and F – Brave type. The X-ray diffraction pattern gives hkl for the F – unit cell for even values, and for I – for h k l = 2n (n is an integer). Transformation centered lattice to P − Bravais types choose that other reflexes do not die but they are absent in reciprocal lattice with metallic crystals are absent.
The definition of the n -order ( n>=2) elastic constants of a loaded crystal and the calculation method of the second and third order elastic constants of hcp crystal under hydrostatic pressure from the energy-deformation relation are given. The energy at the various pressures and deformations of hcp iron is obtained in framework of DFT. The calculations of the second and third order elastic constants of hcp Fe at 20-340 GPa (T=0K) are performed. The Gruneisen parameters for long wave acoustic modes in hcp iron are defined. The obtained results are used for the stability analyses of the hcp phase of iron at high pressures.