Cluster expansion Monte Carlo study of phase stability of vanadium nitrides

Abstract

Phase stability of stable and metastable vanadium nitrides is studied using density functional theory ͑DFT͒ 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 V 2 N to be polymorphic in ⑀-Fe 2 N and -Fe 2 N structures within a few meV and VN to be more stable in WC͑B h ͒ phase than in the experimentally observed NaCl͑B1͒ 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 ⑀-Fe 2 N phase of V 2 N 1−x ᮀ x and NaCl͑B1͒ phase of VN 1−x ᮀ x compared to -Fe 2 N and WC͑B h ͒ phases respectively, rendering the computed phase stability scenario to be in agreement with experiments. Analysis of supercell calculated electronic density of states ͑DOS͒ 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 NaCl͑B1͒ phase of VN 1−x ᮀ x for which measured values are available.

First-principles study of phase stability of stoichiometric vanadium nitrides

“…For the sake of comparison, one notes that our total energy results are very close to those obtained in Ref. 9 for the AsNi-and NaCl-type structures: 101.0 and 181.7 meV/atom, respectively. Based on these results, one can deduce that only WC-type VN can exist at temperatures close to 0 K. We should recall that the triclinic, tetragonal, and cubic structures of VN are experimentally observed at low (< 20 K), moderate (< 205 K) and high temperatures (> 205 K), respectively 4 .…”

“…In particular, according to the first-principles calculations 8,9 , the most stable structure of VN is a hexagonal structure, whereas only cubic, tetragonal, and triclinic phases were detected in experiments 1,2,4 . Therefore, the aim of the present investigation is to account for the structural stability of the experimental phases of stoichiometric vanadium nitride in the framework of a firstprinciples approach.…”

“…The tetragonal phase with the space group P42m was found to transform into another tetragonal phase with the space group P 4 2 /mcm (t-VN) when the band energy smearing associated with temperature decreases 7 . The ground-state and phase stability properties of the cubic and hexagonal phases of VN x have been investigated based on total-energy calculations with a first-principles pseudo-potential method 8,9 . The stoichiometric vanadium nitride was found to have enhanced stability in the WC-type lattice as compared to the experimental NaCltype structure.…”

“…The stoichiometric vanadium nitride was found to have enhanced stability in the WC-type lattice as compared to the experimental NaCltype structure. Also, it was shown that nitrogen vacancies stabilize the NaCl phase of VN x compared to WC phases 9 . The stabilization of the NaCl-type over WCtype transition metal compounds with non-metal vacancies was also established on the basis of an analysis of their electronic structures 10,11 .…”

First-principles calculation of phase equilibrium of V-Nb, V-Ta, and Nb-Ta alloys

“…Detailed illustration of the method can be found in many papers. 18,20,26,[33][34][35][36][37][38][39] Here a brief description of the main aspects is given. In the cluster expansion, the alloy is treated as a lattice problem in which the lattice sites are fixed at those of the underlying Bravais lattice (fcc, bcc, etc.)…”