Role of vibrational entropy in the stabilization of the high-temperature phases of iron

The phonon dispersions of the bcc and fcc phases of pure iron ($\alpha$-Fe, $\gamma$-Fe, and $\delta$-Fe) at ambient pressure were investigated close to the respective phase transition temperatures. In the open bcc structure the transverse phonons along T${}_1\left[\xi \xi 0\right]$ and T${}_1\left[\xi \xi 2\xi \right]$ are of particularly low energy. The eigenvectors of these phonons correspond to displacements needed for the transformation to the fcc $\gamma$ phase. Especially these phonons, but also all other phonons, soften considerably with increasing temperature. Comparing thermodynamic properties of the fcc and the two bcc phases it is shown that the high-temperature bcc phase is stabilized predominantly by vibrational entropy, whereas for the stabilization of the fcc phase electronic entropy provides an equal contribution.

Figure 1

Phonon dispersions of Fe. The solid lines correspond to the expected values of the Born-von Kármán parameters' a posteriori distribution, from which the densities of states have been calculated. Circles (orange) represent measured longitudinal modes, diamonds (green) transverse modes. Triangles (blue) correspond to the T${}_2\left[\xi \xi 0\right]$ and T${}_2\left[\xi \xi 2\xi \right]$ branches, where appropriate.

Figure 2

Debye temperature defined via the vibrational entropy as a function of temperature. The errors are smaller than the symbols.