1. 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

2. 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 nm
Pd nm
Pt 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.

3. 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.

4. 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.

5. 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.

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

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

8. 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.

9. 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.