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Thin films, surfaces and nanomaterials

When an alloy containing dispersed precipitate particles of different sizes in a matrix is held at high temperature for a long time, which correctly describes Ostwald ripening?

  1. ASmaller particles, around which solubility is higher, dissolve and disappear, and their atoms diffuse to larger particles, which grow
  2. BLarger particles, around which solubility is higher, dissolve while smaller particles grow, so the sizes become uniform
  3. CThe average particle size increases solely through particles colliding directly and coalescing
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Answer: A. Smaller particles, around which solubility is higher, dissolve and disappear, and their atoms diffuse to larger particles, which grow

A particle with a small radius of curvature has a chemical potential raised by the interfacial energy, so the equilibrium solubility in the surrounding matrix is higher (the Gibbs–Thomson effect). The solute concentration is therefore high around small particles and low around large ones, and solute diffuses from small particles to large ones. Small particles thus disappear and large ones grow, reducing the total interfacial area (interfacial energy). This is the main cause of softening by overaging in precipitation-strengthened alloys and of the coarsening of nanoparticles. The choice with the solubility relation reversed is wrong, and collision and coalescence of particles is a mechanism distinct from Ostwald ripening.

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  1. Which statement about the surface energy of metal crystals is correct?
  2. 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*?
  3. 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°?
  4. 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?
  5. Among thin-film growth modes, which correctly describes Stranski–Krastanov (SK) growth?