Computational modelling of martesitic transformation of TiPd memory alloys

Abstract

Titanium-based shape memory alloys have attracted a lot of attention due to their important technological applications including actuator devices, electronics, and medical stents. This is due to their shape memory effects (SMEs) and superelasticity. Ti50Pd50 system is considered as one of the potential high temperature shape memory alloy (HTSMA) due to their high martensitic transformation temperature at 823 K. Previous studies revealed that this alloy is mechanically unstable displaying a negative 𝐶′ (𝐶′<0) at 0 K. Furthermore, their strength collapses above 823 K, which results in low ductility, extremely poor shape memory and corrosion resistance. In the current study, multi-scale computational methods were used to investigate the stability and phase transformation of binary Ti50Pd50 and the ternary Ti50Pd50-xMx alloys. The ternary alloying of Ru, Pt, Ir, Co, Ni, Os, Al was carried out to enhance shape memory properties and the transformation temperature of the Ti50Pd50. Firstly, density functional theory was used to investigate the stability of B2, L10, B19 and B19′ Ti50Pd50 shape memory alloys. A plane-wave pseudopotential method within the Perdew-Burke-Ernzerhof Generalized Gradient Approximation (PBE-GGA) was employed. The electronic properties, phonon dispersion curves and elastic constants were determined to check the stability of these alloys. It was found that the lattice parameters and heats of formation are well in agreement to within 5 % with the available experimental and theoretical data. More importantly, B19′ Ti50Pd50 was predicted to be the most stable structure (displaying the lowest heats of formation) as compared to B19, B2 and L10. This observation is consistent with the density of state stability trend. The elastic constants revealed mechanical instability of the B2 phase (𝐶′>0) while L10, B19 and B19′ were found to be stable (𝐶′<0). Furthermore, the B2 phase is vibrationally unstable due to the presence of soft mode emanating from the phonon dispersion curve. Secondly, the supercell approach was used to investigate the effect of ternary alloying with Ru, Os, Pt, Ir, Co, Al and Ni on the B2 Ti50Pd50 structure. A 2x2x2 supercell was used to introduce the various dopants on the Pd sub-lattice. The heats of formation was found to decrease with an increase in Ru, Os, Pt and Ir concentrations (condition of stability), consistent with the density of states trend. This is in contrast to Co, Ni and Al addition which indicates that the thermodynamic stability is not enhanced (heats of formation increases). It was also found that an increase in Os, Ru and Co content stabilizes the Ti50Pd50 with a positive elastic shear modulus (𝐶′>0) above 18.25, 20 and 31 at. %, respectively. The results suggest that these dopants are likely to decrease the martensitic transformation temperature of the Ti50Pd50 alloy. Interestingly, partial substitution of Pd with Ir and Pt was found more effective in strengthening the compound and may enhance the martensitic transformation temperature of the Ti50Pd50 alloy further. The calculated moduli confirm that alloying with Ru, Os and Co effectively enhances the ductility in Ti50Pd50 systems. Anisotropy factor and Vickers hardness are studied and hardness is found to increase with an increase in Ru, Os and Co content. Thirdly, the semi-empirical embedded atom interatomic potentials method incorporated in the LAMMPS code was employed to investigate the temperature dependence of the B19, B19′, B2, L10 binary Ti50Pd50 and ternary B19 Ti50Pd50-xMx (M= Co, Ni) structures. It was found that the B19 Ti50Pd50 gave a c/b ratio of 1.414 at approximately 1496 K which suggests that the B19 has transformed to a cubic B2 phase. Furthermore, the addition of Co and Ni lowers the transformation temperature from the B19 to the B2 phase. The DFTB+ code was used to develop the sets of parameters for Ti50Pd50 and Ti50Pd50-xRux alloys employing the parameterization technique. As part of the validation, the developed set of parameters yielded results such as lattice parameters and bond distances that are in good agreement to within 5 % as compared to DMol3 findings. Furthermore, temperature dependence calculations were performed to determine the transformation temperature of binary Ti50Pd50 and ternary Ti50Pd50-xRux alloys. It was observed that the addition of Ru reduces the transformation temperature of binary Ti50Pd50. Finally, cluster expansion and Monte-Carlo simulations were employed to determine phase changes and high temperature properties of mixed TiPd1-xRux and Ti1-xPdRux shape memory alloys. A total of 27 new structures for the B2 TiPd1-xRux and 17 new structures for B2 Ti1-xPdRux were generated. The ground state line predicted 5 stable structures with negative formation energies for Ti1-xPdRux alloys, suggesting thermodynamic stability. It was found that TiPd2Ru (P4/mmm) is the most thermodynamic stable structure. All formation energies of TiPd1-xRux alloys are positive, showing that there is a miscibility gap in the system and thermodynamic instability. The result showed that Ru prefers being substituted on the Ti-site than the Pd-site. It was found that Ti2PdRu and TiPd2Ru mix at 1600 K and below 1400 K, respectively which were confirmed by the constructed phase diagram of TiPd1-xRux and Ti1-xPdRux. Thus, multi-scale approaches were successfully used to understand the structural, electronic, elastic and vibrational stability, as well as the transformation behaviour of both binary and ternary alloys.