The thermodynamic ordering transformation of tetragonal FeNi system is investigated by the Exact Muffin-Tin Orbitals (EMTO) method. The tetragonal distortion of the unit cell is taken into account and the free energy is calculated as a function of long-range order and includes the configurational, vibrational, electronic and magnetic contributions. We find that both configurational and vibrational effects are important and that the vibrational effect lowers the predicted transformation temperature by about 480 K compared to the value obtained merely from the configurational free energy. The predicted temperature is in excellent agreement with the experimental value when all contributions are taken into account. We also perform spin dynamics calculations for the magnetic transition temperature and find it to be in agreement with the experiments. The present research opens new opportunities for quantum-mechanical engineering of the chemical and magnetic ordering in tetrataenite.
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