Cluster expansion Monte Carlo study of phase stability of vanadium nitrides

Phase stability of stable and metastable vanadium nitrides is studied using density functional theory (DFT) based total-energy calculations combined with cluster expansion Monte Carlo simulation and supercell methods. We have computed the formation enthalpy of the various stable and metastable vanadium nitride phases considering the available structural models and found that the formation enthalpies of the different phases decrease in the same order as they appear in the experimental aging sequence. DFT calculations are known to show stoichiometric V2N to be polymorphic in ϵ-Fe_2N and ζ-Fe2_N structures within a few meV and VN to be more stable in WC(B_h) phase than in the experimentally observed NaCl(B1) structure. As these nitrides are known to be generally nonstoichiometric due to presence of nitrogen vacancies, we used cluster expansion and supercell methods for examining the effect of nitrogen vacancies on the phase stability. It is found that nitrogen vacancies, represented by ◻, stabilize ϵ-Fe_2N phase of V_2N_(1−x◻x) and NaCl(B1) phase of VN_(1−x◻x) compared to ζ-Fe_2N and WC(B_h) phases respectively, rendering the computed phase stability scenario to be in agreement with experiments. Analysis of supercell calculated electronic density of states (DOS) of VN_(1−x◻x) with varying x, shows that the nitrogen vacancies increase the DOS at Fermi level in WC phase, whereas they decrease the DOS in NaCl phase. And this serves as the mechanism of enhancement of the stability of the NaCl phase. Monte Carlo simulations were used for computing the finite temperature formation enthalpies of these phases as a function of nitrogen-vacancy concentration and found close agreement for NaCl(B1) phase of VN_(1−x◻x) for which measured values are available