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Solidification and cast structures

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%).

  1. A0%
  2. BAbout 12%
  3. CAbout 7.8%
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Answer: C. About 7.8%

Writing the remaining liquid fraction as fL = 1 − fs, 33.2 = 4.0 × fL^(−0.83), so fL = (33.2/4.0)^(−1/0.83) = 8.3^(−1.20) ≈ 0.078, about 7.8%. In equilibrium solidification, 4.0 wt%Cu is below the α solubility limit of 5.65 wt%, so the alloy is all α at the end of solidification and no eutectic forms. 0% is the mistake of applying this equilibrium reasoning to real solidification, where diffusion in the solid is slow. About 12% is 4.0/33.2, which assumes that all the copper in the alloy collects in liquid of eutectic composition and ignores the copper left in the solid. Real castings likewise show eutectic containing Al₂Cu between the dendrites even at compositions within the solubility limit, so the solution treatment temperature is chosen below the melting point of this eutectic.

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