Phase Diagrams for Surface Alloys Christensen, A.; Ruban, A. V.; Stoltze, P.; Jacobsen, K. W.; Skriver, H. L.; Nørskov, J. K.; Besenbacher, F. Phys. Rev. B. 1997

Criteria for Alloy Formation PtAu(111) & PdAu(111) Mixing enthalpy M-Au Pd: - (monomers) Pt: + (clusters) Surface free energy Pt (2.504 J/m²) > Pd (1.743 J/m²)> Au (1.63 J/m²) Size effects Au 0.288 nm Pd 0.275 nm Pt 0.277 nm Kinetics Diffusion rates - Estimate island size to be about 5 nm (about 20 atoms in the island going diagonally) paper doesn’t provide scale bars Christensen, A.; et al. Phase Diagrams for Surface Alloys. Phys. Rev. B 1997, 56, 5822. Tyson, W. R.; Miller, W. A. Surface Free Energies of Solid Metals Estimation from Liquid Surface Tension Measurements. Surf. Sci. 1977, 62, 267−276.

Surface Phase Diagram DFT calculates the surface energy (es) as a function of surface composition (x = NB/N) 𝑒 𝑠 = 1 𝑁 𝑠 [𝐸 𝑁 𝑠 𝐴 , 𝑁 𝑠 𝐵 ; 𝑁 𝐴 − 𝑁 𝑠 𝐴 , 𝑁 𝐵 − 𝑁 𝑠 𝐵 −𝐸 0,0; 𝑁 𝐴 , 𝑁 𝐵 At RT diffusion into bulk is slow surface equilibrium Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.

Surface Phase Diagram Segregation energy ( 𝜕 𝑒 𝑠 𝜕 𝑥 𝑠 ) Energy of interchanging B atom (impurity) with an A atom in the surface (-) : stay in surface layer (+) : bulk diffusion Surface mixing energy B-B excess interactions in surface Curvature of deviation from ideal solution (-): repulsive B-B interaction (intermixing) (+): attractive B-B interaction Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.

Segregation Energy (+) Dissolve into bulk (-) Stay on surface B-B Excess Interactions (-) Repulsive - Mixing (+) Attractive – Phase Separate Segregation Energy (+) Dissolve into bulk (-) Stay on surface AgCu(100)  Mix and stay in surface  bulk Separate  driven by strain effects in the surface layer due to the size mismatch Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.

Segregation Energy (+) Dissolve into bulk (-) Stay on surface Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.

Surface Mixing Energy (+) Mix (-) Phase segregate Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.

Segregation energy (eV/atom) Mixing energy (eV/atom) (+) Dissolve into bulk (-) Stay on surface Co Ni Cu Pd Ag Pt Au -0.17 -0.50 -0.67 -1.16 -0.32 -1.03 0.16 -0.25 -0.27 -0.58 0.14 -0.46 0.27 0.12 -0.03 -0.28 0.21 -0.14 0.40 0.22 0.13 -0.30 0.23 0.33 0.35 0.15 0.07 0.52 0.46 0.32 -0.01 0.45 0.26 -0.04 Mixing energy (eV/atom) (+) Mix (-) Phase segregate Co Ni Cu Pd Ag Pt Au -0.03 -0.78 1.06 0.59 2.40 2.68 0.96 1.17 0.99 1.93 2.86 -0.82 0.35 0.85 1.00 0.72 2.19 0.40 0.42 0.19 -0.37 0.22 0.58 0.81 0.33 0.69 0.50 0.27 0.76 0.16 0.03 -0.41 -0.31 1.16 1.20 0.65 0.73 Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.

Relaxation Effects Estimated shift of the curvature of the surface energy curve caused by relaxation effects 𝑠 𝐴 - 𝑠 𝐵 : Wigner-Seitz radii of metal Units: a.u. (atomic units) ~1 a.u. = ~ 0.05 nm Relaxation : change in total energy when the impurity atom and neighboring atoms are allowed to relax Usually, makes the curvature of the surface energy curve more positive (Table III) Christensen, A.; et al. Phys. Rev. B 1997, 56, 5822.