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Original Articles

Generalized surface thermodynamics with application to nucleation

Pages 927-948 | Received 26 Aug 2007, Accepted 26 Feb 2008, Published online: 08 May 2008

References

  • Gibbs , JW . 1961 . The Scientific Papers of J.W. Gibbs , Dover, New York : Vol. 1 . original work published in 1876, 1878 p.55
  • Ref. [1], p.56
  • When Gibbs considered variations in the amount of a component, he expressed them as variations in the mass rather than in the number of moles
  • Ref. [1], p.222
  • Ref. [1], p.193
  • Larché , FC and Cahn , JW . 1985 . Acta Metall. , 33 : 120
  • Mullins , WW and Sekerka , RF . 1985 . J. Chem. Phys. , 82 : 5192
  • Li , JCM , Oriani , RA and Darken , LS . 1966 . Z. Phys. Chem. Neue Folge , 49 : 271
  • Keenan , JH . 1941 . Thermodynamics , 289 New York : Wiley .
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  • Adkins , CJ . 1983 . Equilibrium Thermodynamics , 106 Cambridge : Cambridge University Press .
  • Baylin , M . 1994 . Survey of Thermodynamics , 234 New York : AIP .
  • Gibbs , JW . 1961 . The Scientific Papers of J.W. Gibbs , Dover, New York : Vol. 1 . original work published in 1873, p.40
  • Ref. [1], p.109
  • Ref. [1], p.221
  • Anderson , DM , McFadden , GB and Wheeler , AA . 1998 . Annu. Rev. Fluid Mech. , 30 : 139
  • Ref. [1], p.219
  • Ref. [1], p.225
  • Voorhees , PW and Johnson , WC . 2004 . Solid State Physics , Edited by: Ehrenreich , H and Spaepen , F . Vol. 59 , 2 Amsterdam : Elsevier .
  • Cahn , JW . 1980 . Acta Metall. , 28 : 1333
  • Shuttleworth , R . 1950 . Proc. R. Soc. A , 63 : 444
  • Herring , C . 1953 . Structure and Properties of Solid Surfaces , Edited by: Gomer , R and Smith , CS . Chicago : University of Chicago .
  • Mullins , WW . 1963 . Metal Surfaces Structure, Energetics and Kinetics , 17 Metals Park, OH : American Society for Metals .
  • Cahn , JW . 1979 . Interfacial Segregation , Edited by: Johnson , WC and Blakely , JM . Metals Park, OH : American Society for Metals .
  • Cammarata , RC . 1994 . Prog. Surf. Sci. , 46 : 1
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  • Ref. [1], p.314
  • Ref. [1], p.317
  • Hillert , M . quoted in ref. [6]
  • Equivalently the summation over j is for all components in the system since if j is not an actual component of α
  • If the surface crystal plane of the solid before dissolution has a relatively small atom fraction of components that are not actual components of the α, then atoms of these components will remain on the newly created surface, and a small mole fraction of atoms that were originally in the crystal plane adjacent to the surface plane that can be Gibbs-reversibly varied will be dissolved in order to make the total number of dissolved atoms equal to the number of lattice sites in the original surface crystal layer
  • Alexander , JI and Johnson , WC . 1985 . J. Appl. Phys. , 58 : 816
  • Leo , PH and Sekerka , RF . 1989 . Acta Metall. , 37 : 3119
  • For a general anisotropic surface, defining the two-dimensional infinitesimal surface strain dϵ ij in the standard way, the surface stress tensor fij can be defined by setting the reversible work to introduce a surface strain dϵ ij as Afij dϵ ij = dZ s, so that The surface stress can be related to the open system surface availability σ by noting that for fixed , dZ s = dB s = d(σA) and that dA = Aδ ijdϵ ij , where δ ij is the Kronecker delta, so that These expressions use a Eulerian measure of surface area and strain. Using a Lagrangian measure [20] would lead to fij = (∂σ/∂ϵ ij )
  • Ref. [1], p. 254
  • Wu , DT , Gránásy , L and Spaepen , F . 2004 . MRS Bull. , 29 : 945
  • Abraham , F . 1968 . J. Atmos. Sci. , 25 : 47
  • Ref. [1], p.88
  • Ref. [12], p.215

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