Phase stability study of Pt-Cr and Ru-Cr binary alloys

Abstract

Planewave pseudopotential calculations were conducted to predict the energetics and phase stability of Pt-Cr and Ru-Cr binary alloys. Validation of appropriate number of k-points and planewave energy cut-off was carried out for all studied systems. At the composition of A3B and AB3 (where A = Cr and B = Pt or Ru) phases, the heats of formation determined for five different structures, L12, A15, tP16, DOC and DO′ C are almost of the same magnitude and the relaxed structures show no rotation. We observed that the cubic L12 Pt3Cr is the most stable structure in agreement with the experiments. The results for PtCr3 indicate the negative heat of formation for the A15 phase whereas all the remaining studied phases have positive heats of formation. It is clear that the PtCr3 (A15) is the most stable structure. PtCr (L10) was found to be more stable compared with PtCr (B2) phase. The L12 Pt3Cr, A15 PtCr3 and L10 PtCr phases could be considered as possible coatings to cover the engines which are exposed to aggresive environments. The heats of formation of all studied compositions and phases of Ru-Cr systems are positive, these results suggest that, generally, studied Ru-Cr phases are not stable. The effect of pressure and doping were investigated on A15 RuCr3 structure which was reported to exist at a higher temperature. Elastic constants and moduli were investigated to determine the strength of the PtCr systems. The strength of PtCr L10 is greater than that of B2 phase. The ratio of shear to bulk modulus (G/B) has been used to predict the ductility or the brittleness of the material. It was found that Pt3Cr L12 is the most ductile phase among those considered in this study. The density of states were calculated to further analyze the stability of systems. The magnetic properties of Cr were studied using VASP which predicted an anti-ferromagnetic and a non-magnetic ground state for pure Cr. We have investigated the thermal stability at 0 GPa for different phases of Pt3Cr, PtCr3, PtCr and RuCr3 A15 phase, where we detected the soft modes at X, G, M and R points of the Brillouin zone from the phonon spectra of Pt3Cr A15 phase. Pt3Cr L12 and PtCr3 A15 are predicted as dynamically stable structures. RuCr3 A15 phase was found to be dynamically stable but thermodynamically unstable. Phonon DOS were studied to observe the modes of vibration and atoms that contribute to soft modes. Lastly we investigated the thermal expansion of Pt3Cr L12 and A15 phases.