Solidification of metals

Homogeneous nucleation in a liquid melt occurs when the metal itself provides the atoms needed to form nuclei, in other words the homogeneous nucleation occurs in pure metals without needing of any agents. 

Let us consider the case of a pure metal solidifying, when a pure liquid metal is cooled below its equilibrium freezing temperature(The temperature at which the solidification of the metal occurs) to a sufficient degree, many homogeneous nuclei are created by slow-moving atoms bonding together. 

For a nucleus to be stable so that it can grow into a crystal, it must reach a critical size. A cluster of atoms bonded together that is less than the critical size is called an embryo, and one that is larger than the critical size is called a nucleus. Because of their instability, embryos are continuously being formed and re-dissolved in the molten metal(because it is not stable) due to the agitation of the atoms.

Note that :

Energies Involved in Homogeneous Nucleation

When a pure liquid metal is cooled below its equilibrium freezing temperature, the driving energy for the liquid to solid transformation is the difference in the volume (bulk) free energy ΔGv of the liquid and that of the solid. If ΔGv is the change in free energy between the liquid and solid per unit volume of metal, then the free-energy change for a spherical nucleus of radius r is 4/3π r^3 ΔGv since the volume of a sphere is 4/3πr^3.

The change in volume free energy versus radius of an embryo or nucleus is shown schematically in Figure (2) as the lower curve and is a negative quantity since energy is released by the liquid to solid transformation. However, there is an energy opposing the formation of embryos and nuclei, the energy required to form the surface of these particles.

The energy needed to create a surface for these spherical particles ΔGs is equal to the specific surface free energy of the particle (γ) times the area of the surface of the sphere, or 4πr^2 γ , where 4πr^2 is the surface area of a sphere. This retarding energy ΔGs for the formation of the solid particles is shown graphically in Figure (3). The total free energy associated with the formation of an embryo or nucleus, which is the sum of the volume free-energy and surface free-energy changes, is shown in Figure (2) as the middle curve. 

In equation form, the total free-energy change for the formation of a spherical embryo or nucleus of radius r formed in a freezing pure metal is:

• In nature, a system can change spontaneously from a higher to a lower-energy state.

• In the case of the freezing of a pure metal, if the solid particles formed upon freezing have radii less than the critical radius r*, the energy of the system will be lowered if they re-dissolve. 

• These small embryos which have radii less than the critical radius r* can, therefore, re-dissolve in the liquid metal. However, if the solid particles have radii greater than r*, the energy of the system will be lowered when these particles (nuclei) grow into larger particles or crystals. When r reaches the critical radius r*, ΔGT has its maximum value of ΔG*.

A relationship among the size of the critical nucleus, surface free energy, and volume free energy for the solidification of a pure metal can be obtained by differentiating Equation below. The differential of the total free energy ΔGT with respect to r is zero when r = r* since the total free energy versus radius of the embryo or nucleus plot is then at a maximum and the slope d(ΔGT)/dr = 0. Thus,

Critical Radius versus Undercooling

The greater the degree of undercooling ΔT below the equilibrium melting temperature of the metal, the greater the change in volume free energy ΔGV. However, the change in free energy due to the surface energy ΔGs does not change much with temperature. Thus, the critical nucleus size is determined mainly by ΔGV. Near the freezing temperature, the critical nucleus size must be infinite since ΔT approaches zero. As the amount of undercooling increases, the critical nucleus size decreases. Figure (3) shows the variation in critical nucleus size for copper as a function of undercooling. The critical-sized nucleus is related to the amount of undercooling by the relation:

where:

•  r* = critical radius of nucleus.
• γ = surface free energy.
• ΔHf = latent heat of fusion.
• ΔT = amount of undercooling at which nucleus is formed.

Figure (3)

Heterogeneous Nucleation

Heterogeneous nucleation is nucleation that occurs only by an agent in a liquid such as the surfaces of its container, insoluble impurities, and other structural material that lowers the critical free energy required to form a stable nucleus. Since large amounts of undercooling do not occur during industrial casting operations and usually range between 0.1°C and 10°C, the nucleation must be heterogeneous and not homogeneous.

For heterogeneous nucleation to take place, the solid nucleating agent (impurity solid or container) must be wetted by the liquid metal. Also the liquid should solidify easily on the nucleating agent. Figure (4) shows a nucleating agent (substrate) that is wetted by the solidifying liquid, creating a low contact angle θ between the solid metal and the nucleating agent. Heterogeneous nucleation takes place on the nucleating agent because the surface energy to form a stable nucleus is lower on this material than in the pure liquid itself (homogeneous nucleation). Since the surface energy is lower for heterogeneous nucleation, the total free-energy change for the formation of a stable nucleus will be lower, and the critical size of the nucleus will be smaller. Thus, a much smaller amount of undercooling is required to form a stable nucleus produced by heterogeneous nucleation.

Figure (4)

Growth of Crystals in Liquid Metal and Formation of a Grain Structure

After stable nuclei have been formed in a solidifying metal, these nuclei grow into crystals, as shown in Figure (1). In each solidifying crystal, the atoms are arranged in an essentially regular pattern, but the orientation of each crystal varies. When solidification of the metal is finally completed, the crystals join together in different orientations and form crystal boundaries at which changes in orientation take place over a distance of a few atoms. Solidified metal containing many crystals is said to be polycrystalline. The crystals in the solidified metal are called grains, and the surfaces between them, grain boundaries.

The number of nucleation sites available to the freezing metal will affect the grain structure of the solid metal produced. If relatively few nucleation sites are available during solidification, a coarse, or large-grain, structure will be produced. If many nucleation sites are available during solidification, a fine-grain structure will result. Almost all engineering metals and alloys are cast with a fine-grain structure since this is the most desirable type for strength and uniformity of finished metal products.

When a relatively pure metal is cast into a stationary mold without the use of grain refiners, two major types of grain structures are usually produced:

1. Equiaxed grains (Fine grains).
2. Columnar grains (Coarse grains).

Equiaxed grains

If the nucleation and growth conditions in the liquid metal during solidification are such that the crystals can grow about equally in all directions, equiaxed grains will be produced. Equiaxed grains are commonly found adjacent to a cold mold wall, as shown in Figure (5). Large amounts of undercooling near the wall create a relatively high concentration of nuclei during solidification, a condition necessary to produce the equiaxed grain structure.

Fine or equiaxed grains refer to smaller and more numerous crystal structures that result from rapid cooling or solidification. When a material cools quickly, there is less time for the atoms or molecules to arrange themselves into larger, organized crystal structures. As a result, numerous small grains are formed. Fine-grained materials tend to be more brittle.

Columnar grains

Columnar grains are long, thin, coarse grains created when a metal solidifies rather slowly in the presence of a steep temperature gradient. Relatively few nuclei are available when columnar grains are produced. Equiaxed and columnar grains are shown in Figure (5a). Note that in Figure (5b) the columnar grains have grown perpendicular to the mold faces since large thermal gradients were present in those directions. Fine grains are more brittle.

Coarse grains or Columnar result from slower cooling or solidification processes. Slower cooling allows atoms or molecules more time to arrange themselves into larger, more defined crystal structures. Coarse grains are more ductile and soft.

Figure (5)

Note that :

• In material science coarse grain refer to large grains, and fine refer to small grains.

• Fine-grained materials tend to be more brittle and have high strength.

• Coarse-grained materials tend to be more ductile and have high strength.