Application of the cluster variation method to ε-Fe₂N_1-z and ζ-Fe₂N: Ordering of interstitial atoms

The regular and the irregular trigonal prism approximations of the cluster variation method (CVM) are applied to investigate the ε-Fe₂N_1-z and the ζ-Fe₂N phases. The ε-Fe₂N_1-z/ζ-Fe₂N phase boundary, the types of interstitial ordering and the lattice parameters of the ε and ζ phases are calculated and compared with the available experimental data. In the composition range from 25 to 33 at.% N, long-range order occurs. The changes in the N distributions are associated with the strong repulsive interactions between neighbouring N atoms. The CVM results show that with increasing the N content towards 33 at.% N, the repulsive N-N interactions favour the distortion of the iron host lattice, thereby increasing the nearest-neighbouring distance between occupied sites, i.e. transformation to the ζ-Fe₂N phase. The calculated interstitial site occupations are in good agreement with those proposed on the basis of experimental data obtained by Mössbauer spectroscopy and neutron diffraction.