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Phase Diagrams for Surface Alloys

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. Surface Phase Diagram. DFT calculates the surface energy ( e s ) as a function of surface composition (x = N B /N)

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Phase Diagrams for Surface Alloys

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  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. Surface Phase Diagram • DFT calculates the surface energy (es) as a function of surface composition (x = NB/N) • At RT diffusion into bulk is slow surface equilibrium Christensen, A.; et al. Phys. Rev. B1997, 56, 5822.

  3. Surface Phase Diagram • Segregation energy ) • 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. B1997, 56, 5822.

  4. B-B Excess Interactions (-) Repulsive - Mixing (+) Attractive – Phase Separate Segregation Energy(+) Dissolve into bulk (-) Stay on surface Christensen, A.; et al. Phys. Rev. B1997, 56, 5822.

  5. Segregation Energy(+) Dissolve into bulk (-) Stay on surface Christensen, A.; et al. Phys. Rev. B1997, 56, 5822.

  6. Surface Mixing Energy(+) Mix (-) Phase segregate Christensen, A.; et al. Phys. Rev. B1997, 56, 5822.

  7. Segregation energy (eV/atom) (+) Dissolve into bulk (-) Stay on surface Mixing energy (eV/atom) (+) Mix (-) Phase segregate Christensen, A.; et al. Phys. Rev. B1997, 56, 5822.

  8. Relaxation Effects • Estimated shift of the curvature of the surface energy curve caused by relaxation effects • - : 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. B1997, 56, 5822.

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