Solidification and cast structures
Check the equilibrium partition coefficient and segregation, constitutional supercooling and cells and dendrites, dendrite arm spacing and cooling rate, the Scheil equation, eutectic growth and modification, refinement of cast structures and solidification shrinkage with multiple-choice questions.
Solidification and cast structures: key points
When an alloy solidifies, the solid takes up solute at a different concentration from the liquid, and the ratio of the two is called the equilibrium partition coefficient k. A solute with k < 1 is rejected into the liquid ahead of the interface, which lowers the liquidus temperature there, so with a small temperature gradient constitutional supercooling occurs and a planar interface breaks down into cells or dendrites. The interface shape is set by the ratio of the temperature gradient to the growth rate, G/V, and the fineness of the structure by the cooling rate G×V.
In real solidification, where diffusion in the solid is slow, solute becomes concentrated between the dendrites as the Scheil equation shows, and even alloys within the solubility limit form non-equilibrium eutectic. This microsegregation can be reduced by homogenization annealing, but macrosegregation on the scale of the ingot does not disappear. The proportions of columnar and equiaxed grains in a casting can be changed by the superheat, grain refiners and stirring, and solidification shrinkage and solidification time are the basis of riser design.
All Solidification and cast structures questions (15)
- 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?
- 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?
- 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.
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?
- 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?
- 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%).
- Which is the correct pairing of additions to a hypoeutectic Al-Si casting alloy and their main effects?
- When a regular lamellar eutectic is directionally solidified, the lamellar spacing λ and growth rate V obey λ²V = constant. At a growth rate of 10 µm/s, λ = 2.0 µm. Which is closest to λ when the growth rate is raised to 160 µm/s?
- Take the densities of pure aluminum at its melting point (660 °C) as 2.375 g/cm³ for the liquid and 2.55 g/cm³ for the solid. Which is closest to the decrease in volume relative to the liquid volume (solidification shrinkage) when the liquid turns entirely into solid at the melting point?
- Which combination of methods correctly reduces the columnar zone of an ingot and widens the central equiaxed zone, refining the grains?