Thermodynamics of the hexagonal close-packed iron-nitrogen system from first-principles

DTU Orbit (23/12/2018) Thermodynamics of the hexagonal close-packed iron-nitrogen system from first-principles First-principles thermodynamic models are developed for the hexagonal close-packed ε-Fe-N system. The system can be considered as a hexagonal close-packed host lattice of iron atoms and with the nitrogen atoms residing on a sublattice formed by the octahedral interstices. The iron host lattice is assumed fixed.The models are developed entirely from firstprinciples calculations based on fundamen-tal quantum mechanical calculation through the density functional theory approach with the atomic numbers and crystal structures as the only input parameters. A complete thermody-namic description should, at least in principle, include vibrational as well as configurational contributions. As both contributions are computationally very demanding in first-principles calculations, the present work is divided in two parts, with a detailed accounts of each of these contributions.Vibrational degrees of freedom are described in the quasiharmonic phonon model and the linear response method is applied to determine force constants from first-principles calcula-tions. The hexagonal lattice poses a special challenge as two lattice parameters are required to describe the system. The quasiharmonic phonon model is generalized to hexagonal systems and a numerically tractable extended equation of state is developed to describe thermody-namic equilibrium properties at finite temperature.The model is applied to ε-Fe3N specifically. Through the versatility of the model, equi-librium lattice parameters, the bulk modulus, and the thermal expansion coefficient can be obtained at any temperature of interest. The thermal expansion predicted by the generalized quasiharmonic phonon model is in excellent agreement with experimental data. The model also allows calculation of the volume–pressure relationship at finite temperature, and good agreement with experimental data is obtained also in this case.In the second part, configurational degrees of freedom of the nitrogen occupation of the in-terstitial sites are investigated by thermodynamic statistical sampling, also known as Monte Carlo simulations, where nitrogen atoms are allowed to migrate randomly in a large com-puter crystal according to relative energies of the configurations until chemical equilibrium is reached. Configurational energies are described in an Ising-like cluster expansion determined from a large database of calculated first-principles energies.The model provides a description of collective effects of orderings of atoms and phase transitions observed in large systems. Ensemble average long-range order parameters and the Cowley–Warren short-range order parameters are calculated and provide evidence of specificorderings. The intermediate ε-Fe24N10 nitride is predicted as a ground-state structure andordering consistent with the structure is observed at finite temperature. An ε → ζ phase transition is predicted with phase boundaries is excellent agreement with experimental data.The local environment of the iron atoms can be explicitly calculated in the computer crystal and are compared to recorded Mössbauer spectra. Finally, predictions of phase diagrams from first-principles calculations is demonstrated.