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Thin films, surfaces and nanomaterials

Which statement about the surface energy of metal crystals is correct?

  1. ASurface atoms have lost some bonds, so the surface energy is positive, and it is generally lower on densely packed low-index planes
  2. BSurface atoms have fewer neighbors and can move freely, making them more stable than interior atoms, so the surface energy is negative
  3. CBecause metallic bonding is non-directional, the number of broken bonds does not depend on the plane either, so the surface energy is the same for every crystal plane
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Answer: A. Surface atoms have lost some bonds, so the surface energy is positive, and it is generally lower on densely packed low-index planes

When a crystal is cut to create a surface, the surface atoms lose some of their bonds to neighboring atoms. Their energy rises accordingly, so the surface energy, the excess energy per unit area, is positive. Even though metallic bonding is non-directional, the number of broken bonds depends on the plane; on densely packed planes such as FCC {111}, fewer bonds point out of the plane, so the surface energy is lower. That is why low-index close-packed planes tend to appear in the equilibrium shapes of crystals and in grown particles. Metals with stronger bonds and higher melting points have larger surface energies: about 3 J/m² for tungsten and about 1 J/m² for aluminum.

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More Thin films, surfaces and nanomaterials questions

  1. In homogeneous nucleation, take the free energy change on forming a spherical nucleus of radius r as ΔG = (4/3)πr³ΔGv + 4πr²γ. For an interfacial energy γ = 0.10 J/m² and a free energy change per unit volume ΔGv = −2.0×10⁸ J/m³, which value is closest to the critical nucleus radius r*?
  2. In heterogeneous nucleation, with θ the contact angle between nucleus and substrate, the energy needed to form a critical nucleus is f(θ) = (2 + cosθ)(1 − cosθ)²/4 times that for homogeneous nucleation. Which value is closest to f(θ) for θ = 60°?
  3. At the same undercooling, how does the radius of curvature of the critical nucleus in heterogeneous nucleation compare with the critical nucleus radius in homogeneous nucleation?
  4. Among thin-film growth modes, which correctly describes Stranski–Krastanov (SK) growth?
  5. Let γs be the surface energy of the substrate, γf that of the film and γi the film–substrate interfacial energy. Under which condition is island (Volmer–Weber) growth likely?