Dynamical stability of NiTi under high pressure and high temperature

•We obtained the high temperature phonons under high pressure.•The phonon-phonon interactions are considered.•The dynamical stable region of austenite NiTi in phase diagram is predicted. By using self-consistent ab initio lattice dynamical calculations that go beyond the quasiharmonic approximation, the temperature-dependent phonon spectra are derived by exciting all the lattice vibrations, in which the phonon–phonon interactions are considered. Based on well reproducing the observed high temperature phonon frequencies at zero pressure, we predict the high temperature phonons under high pressure, and obtain the critical temperature, in which the frequencies were promoted from imaginary to real. And then the stable region of austenite NiTi in phase diagram is predicted successfully.