Calculated phase transitions in iron

check out chapter 5 of my PhD thesis for more details of this work.

Introduction

The α (bcc) - γ (fcc) - δ (bcc) phase transitions make iron quite unique among all elements in the periodic table. For a theoretical calculation of phase transitions in iron, we need to take into account both the electronic and vibartional contributions to the free energy. In our work, we first calculate the electronic (magnetic) contribution by performing a thermodynamic integration for the magnetic degrees of freedom from bcc to fcc iron. After that we calculate the vibrational contribution and treat the effect of spin fluctuations on atomic vibrations with the spin-space averaging scheme as this method has been proven valid for calculations of magnon-phonon coupling in iron. We finally obtain the total free-energy difference by summing up the two contributions, and show that the combined effect of the two contributions leads to α (bcc) - γ (fcc) - δ (bcc) in iron.

Conclusion

At low-temperature region (T < 900 K), the gain of the exchange energy due to the ferromagnetic ordering significantly lowers the internal energy in bcc iron, and the electronic contribution plays a dominant role in determining the total free-energy difference. At high-temperature region (T > 900 K), the electronic contribution decreases to the same energy scale with that of the vibrational contribution, and the competition between the two contributions leads to the α (bcc) - γ (fcc) - δ (bcc) phase transitions. our calculated total free-energy difference is in overall good agreement with the CALPHAD data