Composition-Dependent Fe/Cr Mixing Thermodynamics in α-Al₁₂(Fe,Cr)₃Si₂ Intermetallics

Fe/Cr substitution in α-Al₁₂(Fe,Cr)₃Si₂-type intermetallic particles was investigated using first-principles calculations combined with the Debye–Grüneisen model over 0–850 K at zero external pressure. To examine Fe/Cr mixing within the α framework, 238-atom hP238 cells were modeled at x_Cr = 0, 0.239, 0.500, 0.739, and 1.000. At 0 K, static mixing enthalpy was negative at x_Cr = 0.239 and 0.500 but became slightly positive at the highest sampled intermediate Cr fraction, x_Cr = 0.739. The x_Cr = 1.000 model served only as a hypothetical hP238 endpoint. At a homogenization temperature of 813 K, configurational entropy favored Fe/Cr mixing, while the vibrational contribution was positive and partly offset this effect. The resulting mixing free energies were −11.0 and −6.0 meV/atom for x_Cr = 0.239 and 0.500, respectively, and +7.6 meV/atom for x_Cr = 0.739. The results show that low-to-intermediate Cr substitution, including near-equiatomic Fe/Cr occupancy, is thermodynamically favorable within the α framework, whereas the sampled Cr-rich intermediate composition is unfavorable relative to the two modeled hP238 end members.