Fig. 1. Portion of the Fe–Cr solid phase diagram according to Calphad [9]. The dashed line indicates the metastable α–α′ miscibility gap, and the dash-dotted line indicates the Curie temperature.

Fig. 2. The mixing enthalpy curves at 0 K for random or quasi-random ferromagnetic Fe–Cr alloys according to different DFT techniques [16], [19] and [21], as discussed in the text. For comparison, the only existing experimental data, obtained for the paramagnetic phase [56], are also shown.

Fig. 3. Mixing enthalpy at 0 K for the Fe–Cr system according to CDM and 2BM potentials, as well as CE, in the random solution limit, compared with the most recent PAW–SQS data and with the Calphad curve (extrapolated to 0 K from the corresponding free energy expansion). The blow-up shows more in detail the sign-changing curves in the low-Cr region.

Fig. 4. The phase diagram according to the three cohesive models in RSM approximation.

Fig. 5. The function for the three cohesive models.

Fig. 6. Cr–Cr pair repulsive energy according to CDM and 2BM potentials, as well as CE, as compared with DFT data from [18] (54 atoms) and [21] (128 atoms) (The two sets of DFT data were obtained with the same code and approximation, so the difference is fully ascribable to box size effects). The values obtained with the potentials correspond to a fully converged box size.

Fig. 7. Short-range order (SRO) parameter vs. Cr concentration according to simulations performed: (a) using a Metropolis MC method including relaxation with the CDM potential at 700 K [64]; (b) using an atomistic KMC method on rigid lattice with the 2BM potential at 700 K [63]; and (c) using an exchange MC method with the CE [29]. Also given, for comparison, are the corresponding experimental values from [14], as well as the limiting line (dashed), representing the minimum SRO parameter value theoretically possible.

Fig. 8. The heat of formation for the BCC-99 structures calculated using the different cohesive models.

Fig. 9. The phase diagram according to the three cohesive models taking into account full configurational entropy.

Fig. 10. The excess vibrational free energy evaluated with different methods using the 2BM interatomic potential.

Fig. 11. The excess vibrational free energy evaluated with different methods using the CDM interatomic potential.

Fig. 12. The phase diagram according to the interatomic potentials taking into account configurational and vibrational entropy.