New modelling of the B2 phase and its associated martensitic transformation in the Ti–Ni system
Introduction
The Ti–Ni system has been of great interest mainly due to the unique shape memory effect (SME) and the pseudoelasticity (PE) which occur in the near-equiatomic TiNi alloys. In comparison with other shape memory alloys (SMAs), the TiNi SMAs provide the best combination of material properties, e.g. the maximum recoverable strain and stress, excellent corrosion resistance and the best biocompatibility. They are the most widely used SMAs in the world. The unique SME and PE originate from the so-called thermoelastic martensitic transformation. In the Ti–Ni system, it is the intermetallic compound B2 phase that can undergo a thermoelastic martensitic transformation in the composition range around 50 at.% Ni. The phase diagram and thermodynamic properties of the B2 phase and the associated martensitic transformation product phase B19′ are essential not only for understanding the kinetics of the transformation but also for further development of SMAs.
However, the ordinary phase diagram does not include the low temperature phase since it is usually believed that the martensitic transformation product phase is metastable. In the present case, nevertheless, the parent phase B2 is stable down to low temperatures [1], and hence fast cooling is not necessary for preventing its decomposition. Furthermore, it is known that the martensitic transformation takes place regardless of the cooling rate in the Ti–Ni system 2, 3. So we consider that the B19′ phase could be stable. Therefore, our aim was to establish thermodynamic models to describe the parent phase B2 and the low temperature phase B19′ and then study properties related to the transformation, such as the T0 temperature, the Ms temperature, and the transformation enthalpy.
The B2 phase with CsCl crystal structure in the Ti–Ni system has been modelled thermodynamically several times 4, 5, 6, 7, 8. Among the previous works Saunders [7] applied the two-sublattice model with the formula (Ni, Va)0.5(Ni, Ti)0.5 to describe it. This model suggests the major structure imperfections are vacancy defects on the nickel sublattice while the main defects on the titanium sublattice are substitutional Ni atoms. This is in agreement with experimental observation [2]. In fact, this model is a good approximation of reality, but the two sublattices are identical so one should have the same constituents on both. This requirement must also be fulfilled in order to describe the disordering of the B2 phase to the A2 (b.c.c.) phase. In the Ti–Ni system, there is a Ti-rich A2 phase which is the disordered form of the B2 phase and the B2 phase can be considered as an ordered state of the A2 phase. From the physical point of view, A2 and B2 should be described with a single Gibbs free energy expression and not treated as two separate phases. As a consequence, a new model is needed to treat the order–disorder relation between B2 and A2. In addition, the B2 composition range assessed by Saunders [7] differs from experiments [9] by 1 at.% Ti, which is unacceptable for SMAs because shape memory properties are particularly sensitive to composition. Therefore, a reassessment of the B2 phase has been made in the present work in order to have an accurate description of the composition range of the B2 phase.
An attempt to model the B19′ in the Ti–Ni system has been made in our previous work [10] based on Saunders' model and description [7] for the B2 phase. The same model will be used in the present work, but model parameters will be re-evaluated in order to be consistent with the new description of the B2 phase.
Section snippets
B2 and A2 phases
Most SMAs have a superlattice structure with the sublattices of the parent phase being body-centred cubic (b.c.c.), which are called β-phase alloys. The β-phase alloys are generally divided into two groups according to the superlattice or composition ratio. One group is the β2-phase, which has a CsCl-type B2 superlattice and about 50:50 composition ratio. The parent phase in TiNi SMA belongs to this type of superstructure as shown in Fig. 1 [11]: the Ni atoms fill the corners while the Ti atoms
Selection of experimental data and model parameter evaluation
In the thermodynamic models described in the preceding section, there are several model parameters to be determined in the present work. These parameters are evaluated using a computer optimization program available in Thermo-Calc [13], which will search for the best fit to the selected experimental data or estimated quantities. The program can treat different kinds of input data simultaneously by minimizing the sum of squares of the differences between the target and the calculated values.
The calculated Ti–Ni phase diagram
By using the new parameters evaluated for the B2 and low temperature B19′ phases, the Ti–Ni phase diagram was computed as shown in Fig. 6, in which Saunders' descriptions [7] are kept for all other phases, i.e. liquid, α-Ti (h.c.p. A3), γ-Ni (f.c.c. A1), NiTi2, and Ni3Ti. Figure 6 indicates that the phase boundary of B2 is essentially vertical on the Ti-rich side, while it extends towards the Ni-rich side resulting in a large homogeneity range at high temperature. The homogeneity range exhibits
Conclusions
- 1.
By taking into account the order–disorder transition between the ordered B2 phase and the disordered A2 phase in the Ti–Ni system, the symmetric model (Ni, Ti, Va)0.5(Ni, Ti, Va)0.5 was applied to describe the B2 phase. Thermodynamic properties of the B2 phase have been reassessed and particular attention was paid to its composition range that is critical for SME. The present calculation gives a more precise description of the B2 composition range than the previous one [7]. The calculated melting
Acknowledgements
The authors would like to thank Professor Mats Hillert for his stimulating discussions. Financial aid from the Royal Institute of Technology (KTH) is acknowledged.
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