Single-Atom Alloy (SAA) catalysts exhibit superior catalytic performance compared to monometallic and other bimetallic catalysts. However, their synthesis faces challenges, including guest atom aggregation, limited control over deposition of guest atoms over host, and the need for specialized equipment. Therefore, computational prediction and analysis of SAA catalyst formation and stability are essential before synthesis. Despite their significance, research on computational studies of SAA catalyst stability and surface concentration at finite temperatures is limited. The current study introduces a thermodynamic method combining Density Functional Theory (DFT) for ground-state energy calculations with statistical assumptions to account for temperature and configurational effects. Our approach incorporates modified Langmuir-McLean theory and the Metropolis criterion to model guest atom replacement on the surface, allowing the calculation of segregation free energy in dilute binary alloy systems like SAA catalysts. To demonstrate our method, we examine seven metal-(single atom)-host SAA catalysts: Pt-Ni, Ru-Ni, Re-Ni, Pt-Cu, Pd-Cu, Bi-Pd, and Ni-Ru. The guest atom concentration in the bulk was limited to 0.1, considering two nearest-neighbour interactions which is based on composition-dependent elemental distribution and segregation free energy. The surface-dependent elemental distribution predicts surface concentration, associated to the distribution coefficient (Δ), while the segregation free energy (∆Gseg) represents the energy required to replace a host atom with a guest atom. In our study most, systems showed Δ between 0 and 1, indicating SAA site formation. In contrast, Ru-Ni exhibited a Δ > 1, indicating phase separation. The observed ∆Gseg trends were temperature-dependent and independent of guest atom concentrations. A negative ∆Gseg obtained for Pt-Ni, Pt-Cu, and Pd-Cu indicated stable SAA catalysts whereas a stable Ni-Ru catalyst was obtained at 500K and 1200K. Overall, this study offers a thermodynamic stability framework that can aid in designing SAA catalysts for addressing SAA catalyst screening challenges.
