Computational modelling of TiPt and TiPtCo-M (M=Ta, V, Hf) shape memory alloys

Abstract

First-principles density functional theory has been used to study the stabilities of binary TiPt, TiTa, TiNi and TiCo potential shape memory alloys. Furthermore, ternary alloys Ti50Pt50-xMx with V, Ta, Hf and quaternary Ti50(PtCo)50-xTax systems were also investigated. The structural, electronic and mechanical properties were deduced to mimic the stabilities of these alloys. Furthermore, their vibrational stability, x-ray diffraction and temperature dependence have been examined. The structures were subjected to full geometry optimization to obtain equilibrium lattice constants. It was found that the equilibrium lattice parameters for all the binary systems are in good agreement with experimental results to within 5%. The heats of formation (ΔHf) were calculated to determine the thermodynamic stability of the B2 TiM systems. It was revealed that TiPt is the most energetically favourable (most stable) whereas TiTa is the least favourable due to high ΔHf value (less stable). In addition, electronic properties suggest that TiPt, TiNi and TiCo systems are stable with TiTa being the least favourable consistent with the ΔHf. The elastic properties were also calculated to mimic the mechanical stability of these alloys. TiNi, TiCo and TiTa were found to be mechanical stable whereas TiPt is unstable. This behaviour is consistent with the phonon dispersion curves for TiPt and TiCo. TiCo structure, in particular is the most stable in line with the predicted phonon dispersion. The effect of alloying on Ti50Pt50-xMx (M = V, Ta, Hf) ternary system was carried out using the supercell approach. It was observed that the lattice parameters decrease minimally with an increase in V and increases with an increase in Ta and Hf content. The structures ii become thermodynamically less stable with an increase in V, Ta and Hf content, as depicted by heats of formation. The shear modulus (C′) of Ti50Pt50-xMx increases with an increase in M (V, Ta and Hf) concentration suggesting mechanical stability of these alloys. This has been confirmed from the phonon curves where the phonon soft modes are reduced and tend to disappear with increasing content of the alloying elements. Thus the results suggest that the V, Ta and Hf addition reduces the transformation temperatures of the TiPt alloy as indicated by its higher shear modulus C′. Furthermore, it was observed that the lattice parameters of the quaternary system decrease with an increase in Ta content in the system. Thus ΔHf of the B2 and B19 Ti50Pt43.75-xCo6.25Tax and B19 Ti50Pt31.25-xCo18.75Tax alloy system showed that the 6.25 at.% Ta addition is energetically most favourable (ΔHf<0). The DOS behaviour confirms that the 6.25 at.% Ta as least favourable whereas for B19, the 6.25 at.% Ta is most favourable. The elastic constants for B19 and B2 show the positive shear modulus (mechanical stability). Moreover, the phonon dispersions and phonon density of states for the B2 and B19 Ti50Pt43.75-xCo6.25Tax and Ti50Pt31.25-xCo18.75Tax were calculated and are consistent with the elastic constant. The LAMMPS code was employed to investigate the temperature dependence of the B19 Ti50Pt43.75-xCo6.25Tax and Ti50Pt31.25-xCo18.75Tax structures. The martensitic to austenite transformation temperature decreases with an increase in Ta concentration. Temperature variations of the XRD patterns for the B19 are in reasonable agreement with predicted lattice parameters.