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Solidification and cast structures

Most pure metals grow with a smooth, rounded solid–liquid interface, whereas Si and Bi tend to grow bounded by flat crystal faces (facets). Which is the correct guide to explain this difference?

  1. AThe higher the melting point, the harder it is for interface atoms to move, and every substance melting above about 1000 °C grows with facets
  2. BThe lower the thermal conductivity, the harder it is for latent heat to escape from the interface, and locally overheated faces become facets
  3. CThe larger the entropy of fusion (ΔSf/R greater than about 2), the flatter the interface is on the atomic scale, giving facets
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Answer: C. The larger the entropy of fusion (ΔSf/R greater than about 2), the flatter the interface is on the atomic scale, giving facets

In Jackson's theory the roughness of the interface is set by α ≈ ΔSf/R, the entropy of fusion divided by the gas constant. For most metals α is about 1, so the interface is atomically rough and atoms can attach anywhere, and growth proceeds continuously with a small undercooling (non-faceted). For Si, α is large at about 3.6, the interface is atomically flat and atoms can attach only at steps, so the crystal grows bounded by facets and needs a larger undercooling. It is not the melting point that decides this; iron, with a melting point of about 1540 °C, is non-faceted. Thermal conductivity is not a main factor in the shape either. The plate-like eutectic Si in Al-Si alloys is also a result of the faceted growth of Si.

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More Solidification and cast structures questions

  1. Which statement about constitutional supercooling, which causes an initially planar solid–liquid interface to become uneven in directional solidification of an alloy, is correct? Take an alloy with k < 1.
  2. The condition for solidification with a planar interface and no constitutional supercooling is G/V ≥ ΔT₀/D_L (G is the temperature gradient in the liquid at the interface, V the growth rate, D_L the solute diffusion coefficient in the liquid, and ΔT₀ = mC₀(1 − k)/k the freezing range). When an Al-2.0 wt%Cu alloy (magnitude of the liquidus slope m = 3.4 K/wt%, k = 0.17, D_L = 3.0×10⁻⁹ m²/s) is grown at V = 1.0×10⁻⁵ m/s, which is closest to the minimum temperature gradient needed to keep the interface planar?
  3. Which statement about how the shape of the solid–liquid interface and the fineness of the structure change with the temperature gradient G and growth rate V in alloy solidification is correct?
  4. When dendrites grow in cubic (FCC or BCC) metals, which statement about the crystal direction in which the trunks and arms grow, and its effect on the columnar grains of a casting, is correct?
  5. Suppose that the secondary dendrite arm spacing λ₂ in an aluminum alloy casting is related to the cooling rate Ṫ by λ₂ = A·Ṫ^(−1/3). In a region cooled at 1.0 K/s, λ₂ = 50 µm. Which is closest to λ₂ in a region cooled at 125 K/s?