Abstract
In this article, we presented the ab initio calculation of vacancy formation energy according to Schottky in the alloy Mn 3 GaC. Calculations were carried out in the frameworks of the density functional theory (DFT), implemented in VASP software package. For approximation of the exchange-correlation functional, the generalized gradient approximation in the Perdew–Burke–Ernzerhof formulation was used. It was shown that for the alloy under research, the most energetically favorable formation of a vacancy is in the place of C atom; formation of vacancies in places of Mn atoms is also beneficial, whereas the Ga vacancies are energetically unfavorable. Also, the concentration of vacancies at a finite temperature was calculated. It was shown that Mn and C vacancies have almost identical equilibrium concentration at a nonzero temperature; at that, the concentration of Ga vacancies is negligibly small. In addition, elastic moduli for various magnetic orderings (ferromagnetic, noncollinear, and antiferromagnetic) in the alloy under research were calculated. Using the quasi-harmonic Debye model, the Helmholtz free energy curves were constructed. Using these curves, it was also shown that Schottky monovacancies do not destabilize the ferromagnetic phase. Stability of the ferromagnetic phase is due to the large contribution of magnetic entropy to the Helmholtz free energy for the alloy under research.
Highlights
The ternary X3YC carbide phases formed with the participation of d-metals VIIa, VIIIa- subgroups (X) and non-transition elements IIb–VIb-subgroups (Y) have a simple cubic structure of antiperovskitetype [1]
Computational details The total energy of the studied alloy was calculated using the density functional theory implemented in the VASP [12, 13]
Summary Thermodynamic structural and magnetic properties were calculated for Mn3GaC alloy within the density functional theory
Summary
The ternary X3YC carbide phases formed with the participation of d-metals VIIa-, VIIIa- subgroups (X) and non-transition elements IIb–VIb-subgroups (Y) have a simple cubic structure of antiperovskitetype [1]. Calculations of the energy of the crystal containing the vacancy were performed on 90 atomic supercells. The defect formation energy is calculated with the following equations: Bulletin of the South Ural State University Ser. Mathematics.
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