NiTi (also called Nitinol) transforms from cubic (austenite) to monoclinic (martensite), and vice versa, owing to the shape memory effect and superelasticity. Nitinol has a large number of biomedical applications because of its low elastic modulus close to that of natural bone material and good resistance to corrosion and fatigue, in addition to the transformation temperatures of nitinol that are close to body temperature. It has many other important applications, such as in the aircraft industry. In all these important applications, especially medical applications, Nitinol stability is an important factor for safety. Our goal is to study the stability of NiTi by calculating the phonon dispersion relation to obtain an accurate understanding of the mechanically unstable phases of the NiTi alloy.  The dispersion relation for the cubic and monoclinic phases was studied and coded using MATLAB to make a clear consideration of the dispersion relation and its optical and acoustic branches. Moreover, the density of the state and energy from the lattice vibrations were calculated.

     The crystal is found to be stable by the anharmonic part of the interactions. The austenite phase is stable up to (300 K). While it is not above (300 K). Any extra energy due to temperature changes caused the transformation to the martensite phase. The positive phonon modes indicate that the monoclinic phase is stable against energy perturbations. When the thermal vibration energy was calculated for the cubic phase and in the case of the monoclinic phase at T= 300 K. In both cases, it was less than 5 eV. There are no broken bonds owing to the energy of vibration.