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Solidification and cast structures

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.

  1. ARejected solute lowers the liquidus temperature at the interface, and it rises with distance, so if the actual temperature gradient is small the liquid ahead falls below its liquidus temperature
  2. BSolute in the liquid ahead of the interface is absorbed into the solid and depleted, raising the liquidus temperature, so the larger the temperature gradient the more easily the liquid ahead becomes supercooled
  3. CA negative temperature gradient, with temperature falling from the interface into the liquid, arises from the latent heat of solidification, and this thermal undercooling destabilizes the interface only in alloys
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Answer: A. Rejected solute lowers the liquidus temperature at the interface, and it rises with distance, so if the actual temperature gradient is small the liquid ahead falls below its liquidus temperature

With k < 1, solute rejected at the interface piles up ahead of it, so the liquid at the interface is enriched and its liquidus temperature is lower. Away from the interface the concentration returns to the original C₀, so the liquidus temperature rises with distance. If the actual temperature gradient G is smaller than this gradient of the liquidus temperature, a layer of liquid below its liquidus temperature, that is, supercooled liquid, forms ahead of the interface. This is constitutional supercooling, and because small bumps on the interface grow toward the more supercooled side, the planar interface breaks down. The liquid ahead becomes enriched, not depleted, and a larger temperature gradient makes constitutional supercooling less likely. Thermal undercooling from a negative temperature gradient is a separate phenomenon that does not depend on solute and occurs in pure metals as well.

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More Solidification and cast structures questions

  1. 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?
  2. 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?
  3. 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?
  4. 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?
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