The traditional quasiharmonic approximation cannot predict the phase diagram of Ti accu- rately, due to the well-known soften phonon modes of the β-Ti. By means of self-consistent ab initio lattice dynamics （SCAILD） method, in which the effects of phonon-phonon in- teractions are considered, the phonon dispersion relations at finite temperature for Ti are calculated. From the phonon dispersions, we extrapolat the acoustic velocities and harmonic elastic constants. The dynamical stable regions and phase diagram of Ti are also predicted successfully. The results show that SCAILD method can be designed to work for strongly anharmonic systems where the QHA fails.
