The γ-Fe[N] and γ′-Fe4N1−x phase boundaries in high-nitrogen steels: The cube cluster approximation and the effect of vibrational energy contributions

Abstract

Density functional theory (DFT) calculations and the cluster variation method (CVM) are combined to describe the γ-Fe[N] and γ′-Fe4N1−x phase boundaries. A new cluster approximation, the cube cluster, is used in the CVM. The advantage of using cube clusters is that they comprise both the metal and the interstitial sublattices and that a relatively small number of ordered structures needs to be considered. The cube energies are obtained by DFT calculations applying projector augmented wave pseudo-potentials wherein the electronic structure calculations are carried out in the generalized gradient approximation. The zero-point energy (ZPE), computed using the direct method, changes only slightly the total energy but it increases the cell volumes and decreases the bulk modulus of the cubes. Finite temperature effects are included through the Debye–Grüneisen model. Including the effects of ZPE and finite temperature effects, are necessary to predict the γ-Fe[N] and γ′-Fe4N1−x phase boundaries well.