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Solidification and cast structures

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?

  1. ATrunks and arms grow along perpendicular <100> directions, and grains with <100> nearly opposite to the heat flow outgrow the rest, so the columnar grains have a <100> texture
  2. BTrunks and arms grow along the close-packed <110> direction, in the same direction as slip, so the columnar grains have an easily deformed <110> texture
  3. CTrunks and arms grow along <111>, normal to the close-packed planes, and grains oriented parallel to the mold wall survive preferentially, so the columnar grains have a <111> texture parallel to the wall
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Answer: A. Trunks and arms grow along perpendicular <100> directions, and grains with <100> nearly opposite to the heat flow outgrow the rest, so the columnar grains have a <100> texture

In cubic metals both the trunks and the arms of dendrites grow along <100> directions, with arms at right angles to each other. Slight anisotropy in the interface energy and in how easily atoms attach makes <100> the fastest-growing direction. Among the randomly oriented chill grains formed at the mold wall, those whose <100> is nearly opposite to the heat flow (perpendicular to the wall) advance first, block the inclined grains and outgrow them. As a result of this competitive growth, the columnar grains have a texture with <100> aligned along the growth direction. <110> is the slip direction of FCC and <111> is the normal to the close-packed {111} planes of FCC; neither is a dendrite growth direction. In HCP metals the growth directions are, for example, directions within the basal plane.

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More Solidification and cast structures questions

  1. 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?
  2. Segregation in castings and ingots includes microsegregation, on the scale of the spaces between dendrite arms, and macrosegregation, on the scale of the whole ingot. Which statement about the difference between them is correct?
  3. Suppose Chvorinov's rule t = B(V/A)² holds (t is the solidification time, V the volume, A the surface area and B a constant). Under the same mold conditions, a cube-shaped casting of a certain volume solidified in 10 minutes. Which is closest to the solidification time of a spherical casting of the same volume?
  4. Which is a correct assumption behind the Scheil equation Cs = kC₀(1 − fs)^(k−1) (fs is the fraction solid), which gives the composition of the solid forming during solidification?
  5. An Al-4.0 wt%Cu alloy is solidified. Assume the Scheil equation holds (equilibrium partition coefficient k = 0.17, constant), so the concentration of the remaining liquid rises as CL = C₀(1 − fs)^(k−1). Which is closest to the fraction of liquid remaining when the liquid reaches the eutectic composition of 33.2 wt%Cu (this becomes non-equilibrium eutectic)? On the equilibrium phase diagram, this composition lies within the maximum solubility of the α phase (5.65 wt%).