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Lattice dynamical methods used to predict phase transformations in crystalstypically deal with harmonic phonon spectra and are therefore not applicable inimportant situations where one of the competing crystal structures is unstablein the harmonic approximation, such as the bcc structure involved in the hcp tobcc martensitic phase transformation in Ti, Zr and Hf. Here we present anexpression for the free energy that does not suffer from such shortcomings, andwe show by self consistent {\it ab initio} lattice dynamical calculations(SCAILD), that the critical temperature for the hcp to bcc phase transformationin Ti, Zr and Hf, can be effectively calculated from the free energy differencebetween the two phases. This opens up the possibility to study quantitatively,from first principles theory, temperature induced phase transitions.

Temperature driven $\alpha$ to $\beta$ phase-transformation in Ti, Zr and Hf from first principles theory combined with lattice dynamics