# Ab Initio Study of Martensitic Transformation in NiTiPt High Temperature Shape Memory Alloys
## 3 Results and Discussion
### Phase Stabilities of Ti\({}_{50}\)Ni\({}_{50-x}\)Pt\({}_{x}\) Alloys  
Before rationalizing the strong dependence of the martensite start temperature on alloy composition in ternary Ni-Ti-Pt shape memory alloys from first-principles calculations, we examine the transformation pathways of Ti\({}_{50}\)Ni\({}_{50-x}\)Pt\({}_{x}\) alloys (\(x\) = 0, 6.25, 8.33, 10.42, 12.5, 18.75, 25).  
In Figure 4, we plot the calculated \(E_{\text{f}}\) as a function of the Pt concentration. The binary NiTi alloy can be considered as a TiNiPt alloy containing zero at.% Pt. Above all, as can be seen from Figure 4, in equiatomic NiTi binary alloys, the B2 phase, which is only stable at high temperatures, exhibits the highest value of \(E_{\text{f}}\); the B19\({}^{\prime}\) martensitic structure with the lowest formation energy is the most stable one. They are in excellent agreement with the previous experimental observations [67] and computational results [48].  
Furthermore, the overall trend as presented in Figure 4 shows that the \(E_{\text{f}}\) of B2, B19, and B19\({}^{\prime}\) decline almost linearly with the increasing of Pt doping concentration, which indicates that the stability of Ti\({}_{50}\)Ni\({}_{50-x}\)Pt\({}_{x}\) alloys becomes better when Ni is replaced by Pt. This can be explained by the electronic hybridization of Pt with Ti and Ni (see Figure 5), and will be discussed in more detail in Section 3.3. We can also note that B2 exhibits the highest formation energy which is one of the most unstable structures among all the structures in the TiNiPt system.  
Finally, as shown in Figure 4, when Pt content is between 0 and 12.5 at.%, \(E_{\text{f}}\) of monoclinic B19\({}^{\prime}\) phases are all negative and lower than that of orthorhombic B19 and B2 phases, thus the most stable phase is the monoclinic martensitic crystal structure. However, as Pt content reaches to near 15 at.%, the orthorhombic phases are more stable compared with the monoclinic phases. It can be seen that the \(E_{\text{f}}\) curve of B19 is a little steeper than that of B19\({}^{\prime}\), thus a crossover exists for Pt content about 15 at.%, which can be attributed to the different bond lengths of Ni-Ti in B19 and B19\({}^{\prime}\). The shortest Ni-Ti bond length of B19\({}^{\prime}\) (2.514 A) is smaller than that of B19 (2.564 A), which leads to slightly more repulsive interaction in B19\({}^{\prime}\) compared to that of B19 with the doping of Pt atoms.  
Figure 3: Pt content dependence of (**a**) ’\(a\)’ lattice parameter, (**b**) ’\(b\)’ lattice parameter (**c**) ’\(c\)’ lattice parameter, and (**d**) unit cell volume in B2, B19 and B19\({}^{\prime}\) structures of Ti\({}_{50}\)Ni\({}_{50-x}\)Pt\({}_{x}\) alloys.  
Figure 4: The formation energies, \(E_{\rm f}\) of the austenite B2, martensite B19 and B19\({}^{\prime}\) phases as a function of Pt content in ternary Ti\({}_{50}\)Ni\({}_{50-x}\)Pt\({}_{x}\) alloys.  
Figure 5: Partial density of states (PDOSs) of martensite (**a**) B19\({}^{\prime}\) and (**b**) B19 phase of Ti\({}_{50}\)Ni\({}_{50-x}\)Pt\({}_{x}\) (\(x=0\), 12.5, 18.75) alloys for the Ti, Ni, and Pt site. The vertical line denotes the Fermi level, which is located at 0 eV.  
Therefore, it can be expected that the transformation path would be B2 to B19\({}^{\prime}\) at Pt content less than about 15 at.%, while B2 to B19 at Pt content greater than 15 at.%. As the experimental observations [10] show that, at \(\leq\) 10 at.% Pt, the martensite structure is monoclinic B19\({}^{\prime}\), at higher levels of Pt, at least 16 at.% or greater, the martensite orthorhombic B19 is formed. This means that our calculated result is consistent with the experimental result.