CommunicationTheoretical investigation of structural and mechanical stability of Mo2N
Introduction
Transition–metal nitrides (TMNs) display a wide range of electronic, mechanical and chemical properties which are promising for technological applications, such as hard wear-resistant coatings, diffusion barriers in microelectronics, protective decorative coatings and energy storage [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]]. Molybdenum nitrides are fascinating materials, which all known phases are superconducting, they also exhibit other excellent properties depending on their phase composition [14,15]. The equilibrium phase diagram of molybdenum-nitrogen proposed by Jehn [16], enriched by computed phases of non-stoichiometric transition metal nitrides Mo3N2, shows three stable phases: the tetragonal β-Mo2N phase at low temperature, the cubic γ-Mo2N phase stable at high temperature and the hexagonal δ-MoN phase up to 50 at.% nitrogen concentration.
A great deal of experimental works focus on the synthesis and characterization of the superconducting Mo–N systems [[17], [18], [19], [20], [21], [22], [23], [24], [25], [26]], especially γ-Mo2N as a hard-coat material [[27], [28], [29], [30], [31], [32], [33]]. Although theoretical studies based on first-principles calculations focus on predict of the most stable phases. K. Balasubramanian et al. [34] studied phase stability and mechanical properties of Mo1-xNx with . Eight molybdenum nitride compound phases are found to be thermodynamically stable: tetragonal β-Mo3N, hexagonal δ-Mo3N2, cubic γ-Mo11N8, orthorhombic ε-Mo4N3, cubic γ-Mo14N11, monoclinic σ-MoN and σ-Mo2N3, and hexagonal δ-MoN2. M. B. Kanoun et al. [35] calculated the structure and mechanical stability of all possible cubic and hexagonal structures of MoN, and revealed that the hexagonal phases δ1 and δ3 are more stable energetically than the cubic phases. S. Yu et al. [36] examined thermodynamic, mechanical and dynamical stabilities of Molybdenum dinitride (MoN2). Their results showed that the pernitride MoN2 in both hexagonal P63/mmc and tetragonal P4/mbm structures is mechanically and dynamically stable.
F. F. Klimashin [37] analyzed the impact of nitrogen vacancies on structure and mechanical properties of Mo–N coatings, and found that the higher nitrogen contents favor the ordering of the vacancies at the nitrogen sublattice (hence, γ′-MoNx). The highest hardness of ~33 GPa is obtained for single-phase cubic-structured γ-MoN0.53 coatings.
However, the stability of Mo2N is not established, although the cubic γ -Mo2N is the most common experimentally observed phase of molybdenum nitride. Therefore, it is useful to study the structural and mechanical stability in this system.
In the present investigation, the electronic structure, structural and mechanical stability of Mo2N have been investigated using the first principles calculations for two different phases: γ-Mo2N and β-Mo2N.
Section snippets
Computational details
In this paper, the calculations were performed by the first principles density functional theory (DFT) [38,39] within the Vienna ab initio simulation package (VASP) [[40], [41], [42]]. The ultrasoft pseudo-potential and the generalized gradient approximation (GGA) were used to describe the electron-core interaction and exchange-correlation potentials [43,44], respectively. All calculations were performed with the plane-wave cutoff energy of 380 eV. The valence electron configurations of Mo and
Crystal parameters and phase stability
Mo2N crystallizes in two crystal forms: γ-Mo2N and β-Mo2N. The γ-Mo2N phase is cubic of NaCl–B1-type and belongs to the Fm m space group space, as shown in Fig. 1(a). It can be described as a face centered cubic array of Mo atoms with N atoms randomly occupying one half of the octahedral interstices of the host metal. The β-Mo2N phase is a face centered tetragonal structure of Mo atoms with an ordered array of nitrogen atoms (space group of I41/amd). This structure is considered as a
Conclusion
In this investigation, the electronic structure, thermodynamic properties, structural and mechanical stability of Mo2N have been systematically investigated using the first principles calculations. According to the structural configuration, we consider two possible phases: cubic γ -Mo2N and tetragonal β-Mo2N. The calculated results show that the cubic and tetragonal structures are thermodynamically stables, but β-Mo2N is most energetically stable. The calculated bulk modulus B, shear modulus G,
Declaration of competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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