An Evaluation of the Fe-N Phase Diagram Considering Long-Range Order of N Atoms in γ'-Fe4N1-x and ε-Fe2N1-z

The chemical potential of nitrogen was described as a function of nitrogen content for the Fe-N phases α-Fe[N], γ'-Fe4N1-x, and ε-Fe2N1-z. For α-Fe[N], an ideal, random distribution of the nitrogen atoms over the octahedral interstices of the bcc iron lattice was assumed; for γ'-Fe4N1-x and ε-Fe2N1-z, the occurrence of a long-range ordered distribution of the nitrogen atoms over the octahedral interstices of the close packed iron sublattices (fcc and hcp, respectively) was taken into account. The theoretical expressions were fitted to nitrogen-absorption isotherm data for the three Fe-N phases. The α/α + γ', α + γ'/γ', γ'/γ' + ε, and γ' + ε/ε phase boundaries in the Fe-N phase diagram were calculated from combining the quantitative descriptions for the absorption isotherms with the known composition of NH3/H2 gas mixtures in equilibrium with coexisting α and γ' phases and in equilibrium with coexisting γ' and ε phases. Comparison of the present phase boundaries with experimental data and previously calculated phase boundaries showed a major improvement as compared to the previously calculated Fe-N phase diagrams, where long-range order for the nitrogen atoms in the γ' and ε phases was not accounted for

Thermodynamics and Long-Range Order of Interstitials in a Hexagonal Close-Packed Lattice

Statistical thermodynamics was applied to describe long-range order (LRO) of interstitial atoms in a hexagonal close-packed (hcp) host lattice. On the basis of the Gorsky-Bragg-Williams (GBW) approximation and a division of the interstitial sublattice into six interpenetrating sublattices, all the possible ordered configurations were derived for this assembly. Special attention was devoted to two of the possible ordered configurations of interstitial atoms, viz., the two ground-state structures that have been indicated for ε-Fe2N1-z. A description of the order-disorder transition was obtained, and the evolution of the occupancies of the different types of interstitial sites on changing the total interstitial content was given. Composition-temperature regions of stability for the two ordered configurations were given in phase diagrams for different combinations of pairwise interaction energies. The results are compatible with observations for ε-Fe2N1-z as reported in the literature. The advantages of the present treatment were discussed relative to an earlier one, which a priori excluded nearest neighboring interstitial sites from simultaneous occupancy.

Thermodynamics and Long-Range Order of Nitrogen in γ'-Fe4N1-x

Models are given for the description of the chemical potential of nitrogen in γ'-Fe4N1-x. In previous work, γ'-Fe4N1-x was treated as a (sub)regular solution, thereby assuming that the N atoms are distributed randomly on the sites of their own sublattice. However, in γ'-Fe4N1-x, long-range ordering occurs of the N atoms over the sites of their own sublattice. Then, the expression for the configurational entropy should account for the occurrence of ordering. In the present article, the descriptions adopted and tested for γ'-Fe4N1-x are based on a Langmuir-type approach, the Wagner-Schottky (WS) approach, and the Gorsky-Bragg-Williams (GBW) approach. Application of the various models to data of nitrogen-absorption isotherms for the γ' iron-nitride phase shows that the subregular solution concept fails to describe the experimental data satisfactorily, whereas a very good agreement between theory and experiment is obtained for the WS and GBW approaches. It is shown that, in particular, accounting for the occupation of disorder (octahedral) sites by N atoms is necessary to obtain an accurate description of the chemical potential of nitrogen in γ'-Fe4N1-x.