Thermodynamics and long-range order of nitrogen in γ′-Fe₄N_1-x

Abstract

Models are given for the description of the chemical potential of nitrogen in γ′-Fe₄N_1-x. In previous work, γ′-Fe₄N_1-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′-Fe₄N_1-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′-Fe₄N_1-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′-Fe₄N_1-x.