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Solidification and cast structures

In alloy solidification, the ratio k = Cs/CL of the solute concentrations in the solid and the liquid at the solid–liquid interface is called the equilibrium partition coefficient. Which statement is correct for a case such as Al-Cu alloys, where k is about 0.17?

  1. AThe solid takes up more solute than the liquid, so the regions that solidify first are richest in solute and the regions that solidify last contain the least
  2. BThe solid can take up only about 0.17 times the solute in the liquid, so solute is rejected into the liquid ahead of the interface and the regions that solidify last are richest in solute
  3. CIt is the ratio of the solute diffusion coefficients in the solid and the liquid; at 0.17 diffusion in the solid is slower than in the liquid, but the composition evens out by itself after solidification
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Answer: B. The solid can take up only about 0.17 times the solute in the liquid, so solute is rejected into the liquid ahead of the interface and the regions that solidify last are richest in solute

k is the ratio of the solidus and liquidus compositions at the same temperature on the phase diagram, and it is less than 1 in systems where both the liquidus and the solidus fall toward the solute-rich side. The first solid to form in an Al-4%Cu alloy contains only about 0.17 × 4 = 0.68% Cu, and the excess solute is rejected into the liquid, which gradually becomes richer, so the dendrite cores are lean and the interdendritic regions and grain boundaries that solidify last are rich. Regions that solidify first being richest in solute is the case k > 1. k is not a ratio of diffusion coefficients, and because diffusion in the solid is slow, the concentration differences do not vanish by themselves after solidification; heat treatment is needed to homogenize them. The farther k is from 1, the larger the segregation, and zone refining makes use of this property.

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More Solidification and cast structures questions

  1. 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?
  2. 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.
  3. 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?
  4. 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?
  5. 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?