A state in which solute piled up ahead of the solidification front changes the liquidus temperature so that the actual temperature is below it. It causes a planar interface to break down into cells or dendrites.
Japanese name: 組成的過冷
Constitutional supercooling appears in 4 practice questions across 1 topic, including Solidification and cast structures.
When an alloy with k < 1 solidifies, solute rejected at the interface accumulates in the liquid ahead of it, and the balance with diffusion carrying it away creates a layer whose concentration falls off exponentially from the interface. Since the liquidus temperature depends on concentration, it is low at the interface and rises with distance up to the liquidus temperature of the original composition. If the actual temperature gradient G, rising linearly from the interface, is smaller than this gradient of the liquidus temperature, a layer forms ahead of the interface that is still liquid although it is below its liquidus temperature. Because the supercooling arises from the distribution of composition rather than temperature, it is called constitutional supercooling.
A planar interface is stable when the gradient of the liquidus temperature at the interface does not exceed the actual temperature gradient, which can be written G/V ≥ ΔT₀/D_L. V is the growth rate, D_L the solute diffusion coefficient in the liquid and ΔT₀ = mC₀(1 − k)/k the freezing range. More solute, k farther from 1, faster growth and a smaller temperature gradient all make constitutional supercooling more likely. In real alloys the right-hand side is very large, so under ordinary casting conditions a planar interface can hardly be maintained and solidification proceeds with cells or dendrites. A more rigorous treatment, which also includes stabilization by interface energy, is the Mullins–Sekerka theory.
While the constitutional supercooling is small, bumps on the interface extend only a little, forming cells arranged in a hexagonal pattern; as the supercooling grows, they change into branched columnar dendrites. When it becomes even larger, crystals form and grow in the liquid far ahead of the interface, giving equiaxed dendrites. This is why equiaxed grains form easily in solute-rich alloys and in the centers of castings, where the temperature gradient is small. In single-crystal growth and directionally solidified blades, the temperature gradient is kept large and the growth rate small to maintain the desired interface shape.
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.
Answer: B. About 1.1×10⁵ K/m
The freezing range is ΔT₀ = 3.4 × 2.0 × (1 − 0.17)/0.17 ≈ 33.2 K. The required gradient is G = ΔT₀V/D_L = 33.2 × 1.0×10⁻⁵/(3.0×10⁻⁹) ≈ 1.1×10⁵ K/m, or about 110 K/mm. About 1.9×10⁴ K/m comes from taking ΔT₀ as mC₀(1 − k) and forgetting to divide by k, and about 1.1×10² K/m mistakes the number for 110 K/mm as K/m. Temperature gradients in ordinary casting are of the order of 10³ to 10⁴ K/m, so an alloy can rarely keep a planar interface and solidifies with cells or dendrites. Directional solidification with a planar interface is used in experiments and crystal growth with a large temperature gradient and a very small growth rate.
Not without solute. However, if there is a negative temperature gradient, with temperature falling into the liquid, dendrites grow even in pure metals because of thermal undercooling. Crystals growing freely in an undercooled liquid are an example.
At the edge of the weld pool the temperature gradient is large and the growth rate small, so the interface is close to planar or cellular, while toward the center the gradient falls and the growth rate rises, giving dendrites. This is why the structure of the weld metal changes from place to place.
Yes. The smaller C₀, the narrower the freezing range ΔT₀ and the smaller the G/V needed to keep the interface planar. This is why single crystals of high-purity materials are easier to grow.
This is constitutional supercooling, and because small bumps on the interface grow toward the more supercooled side, the planar interface breaks down.
Which statement about constitutional supercooling, which ca…As the condition for constitutional supercooling shows, the interface shape is set mainly by G/V, and a larger G/V makes a planar interface more stable.
Which statement about how the shape of the solid–liquid int…Reducing solute to narrow the freezing range lowers the constitutional supercooling, which also favors columnar growth.
Which combination of methods correctly reduces the columnar…Dendrite Diffusion coefficient Columnar grains Chvorinov's rule Dendrite arm spacing Equilibrium partition coefficient Eutectic modification Macrosegregation Scheil equation