MME504 — Solidification and Foundry Technology: Lecture Note

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Course code: MME 504 Course title: Solidification and Foundry Technology Course credit load: 2 Units Series 1: Nucleation and Growth of the Solid Phase in Solidification • Part 1.1: The Freezing Process and Its Driving Force o Sub Part 1.1.1: Solidification as a Liquid-to-Solid Transformation o Sub Part 1.1.2: Thermodynamic Driving Force for Freezing o Sub Part 1.1.3: Cooling Curves and Undercooling in Pure Metals • Part 1.2: Nucleation of the Solid Phase o Sub Part 1.2.1: Homogeneous Nucleation and the Critical Radius o Sub Part 1.2.2: Heterogeneous Nucleation on Foreign Surfaces o Sub Part 1.2.3: Nucleation Rate and the Effect of Undercooling • Part 1.3: Growth of the Solid Phase o Sub Part 1.3.1: The Solid-Liquid Interface and Atomic Attachment o Sub Part 1.3.2: Heat Flow and Growth in Pure Metals o Sub Part 1.3.3: Growth Kinetics and Growth Rate • Part 1.4: Grain Formation and the Kinetics of Freezing o Sub Part 1.4.1: Nucleation and Growth Acting Together o Sub Part 1.4.2: Grain Refinement by Inoculation and Cooling o Sub Part 1.4.3: Fraction Solidified and the Time Course of Freezing Introduction Pour molten aluminium into a cold mould and, within minutes, a shapeless liquid becomes a rigid solid whose hidden crystal structure will decide how the finished part behaves. That change is neither instant nor uniform, because it begins at countless tiny points and spreads outward until

the whole casting is solid. Knowing how those points appear, and how the solid then advances into the liquid, is the foundation on which solidification and foundry technology rest. The aim of this Series is to equip you to explain how a liquid metal begins to freeze, how solid nuclei form and grow, and how these two processes together determine the grain structure of the solid. We shall commence with the freezing process and its driving force, including latent heat, undercooling and the cooling curve of a pure metal. Next, we will explore nucleation of the solid phase, comparing homogeneous and heterogeneous routes and the effect of undercooling on the nucleation rate. Afterwards, we will turn to growth of the solid phase, looking at the solid-liquid interface, heat flow and growth rate. We will conclude with grain formation and the kinetics of freezing, covering grain size, inoculation and the rate at which a melt turns solid. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: explain the freezing of a metal as a liquid-to-solid transformation that releases latent heat, • SLO 1.2: explain the driving force for freezing and interpret the cooling curve of a pure metal, • SLO 1.3: explain homogeneous nucleation, including the critical radius and the free energy barrier, • SLO 1.4: compare homogeneous and heterogeneous nucleation and describe how undercooling affects the nucleation rate, • SLO 1.5: describe the solid-liquid interface and the mechanisms of atomic attachment during growth, • SLO 1.6: discuss how heat flow and interface kinetics control the growth rate of a pure metal, • SLO 1.7: explain how nucleation and growth together form grains and how grain size is controlled, and • SLO 1.8: apply the Avrami relation to calculate the fraction of a melt solidified with time.

1.1 The Freezing Process and Its Driving Force 1.1.1 Solidification as a Liquid-to-Solid Transformation Solidification, also called freezing, is the change of a metal from the liquid to the solid state as it cools. In the liquid, atoms move freely and have only short-range order, whereas in the solid they occupy fixed positions in a regular crystal lattice. The change proceeds in two overlapping stages: the formation of tiny stable crystals called nuclei, and the growth of these crystals until no liquid remains. A pure metal freezes at one fixed temperature, its melting point Tm. Because atoms in the solid are arranged more regularly and bonded more strongly than in the liquid, energy is released on freezing. This energy leaves as heat, called the latent heat of fusion, which is the heat given out when unit mass of liquid changes to solid at constant temperature. The latent heat must be carried away through the mould before freezing can finish, so it governs how fast any casting solidifies. Worked example: The latent heat of fusion of copper is about 205 kilojoules per kilogram, so a 5 kilogram copper casting must lose 5 × 205 = 1025 kilojoules, or about 1.0 megajoule, while it freezes. Application: Foundry engineers use the latent heat of fusion to estimate how long a casting will take to freeze and how much heat the mould must absorb. Fill in the blank: The heat given out when a liquid changes to a solid at its melting point is called the __________ heat of fusion. 1.1.2 Thermodynamic Driving Force for Freezing Whether a liquid freezes depends on the Gibbs free energy, G = H − TS, the energy function that a system tries to minimise at constant temperature and pressure. At the melting point Tm the liquid and solid have equal free energy, so neither is favoured and no net freezing occurs. Below Tm the solid has the lower free energy, and the difference between the two, per unit volume, is the driving force for freezing. It is zero at Tm and grows as the metal is cooled further below it. This driving force is estimated by ΔGv = ΔHf ΔT/Tm, where ΔHf is the latent heat of fusion per unit volume and ΔT = Tm − T is the undercooling, the number of degrees by which the liquid is cooled below its melting point. A liquid held exactly at Tm cannot freeze, because there is no driving force. Only when the liquid is undercooled does freezing become possible, and the greater the undercooling, the stronger the tendency to freeze. Worked example: For copper, Tm = 1356 K and ΔHf ≈ 1.8 × 10⁹ J/m³. At ΔT = 20 K, ΔGv = 1.8 × 10⁹ × 20/1356 ≈ 2.7 × 10⁷ J/m³, whereas at ΔT = 230 K, ΔGv ≈ 3.05 × 10⁸ J/m³, which is about 11 times larger. Application: The relation shows why melts that are cooled quickly, and so undercool more, have a much stronger tendency to freeze than those cooled slowly.

Fill in the blank: The number of degrees by which a liquid is cooled below its melting point is called the __________. 1.1.3 Cooling Curves and Undercooling in Pure Metals A cooling curve is a graph of the temperature of a cooling metal against time, and it is the simplest record of freezing. For a pure metal it has three parts: the liquid cools steadily, the temperature stays constant at the freezing point while the latent heat is removed, and the solid then cools again. The flat portion is called the thermal arrest, and its length shows how long freezing takes. Its level identifies the melting point of the metal. In real melts the liquid often cools a little below Tm before the first solid forms. As soon as freezing begins, latent heat is released faster than it is removed, and the temperature rises back to Tm in a sudden jump called recalescence. The temperature then remains at Tm until the last liquid has frozen. The depth of the dip below Tm is a direct measure of the undercooling that the melt needed before nuclei could form. Worked example: Aluminium melts at 660 °C and its latent heat is about 397 kJ/kg. A 2 kg casting dips to 652 °C, so its undercooling is 8 K, and if heat is extracted at 2 kJ/s the arrest lasts 2 × 397/2 = 397 s, about 6.6 minutes. Application: Thermal analysis of cooling curves is used in foundries to check melting points and to detect the degree of undercooling in a melt. Fill in the blank: The sudden rise in temperature after undercooling, caused by the release of latent heat, is called __________.

Figure 1.1: Cooling curve of a pure metal showing undercooling, recalescence and thermal arrest. Pilot questions 1.1 1. Define solidification. (Linked to SLO 1.1) 2. What is the latent heat of fusion? (Linked to SLO 1.1) 3. Why can a liquid held exactly at its melting point not freeze? (Linked to SLO 1.2) 4. Write the expression for the driving force of freezing per unit volume. (Linked to SLO 1.2) 5. What is recalescence, and why does it occur? (Linked to SLO 1.2) 1.2 Nucleation of the Solid Phase 1.2.1 Homogeneous Nucleation and the Critical Radius Homogeneous nucleation is the formation of solid nuclei within a pure liquid, with no help from foreign surfaces. Small clusters of atoms with crystal-like order, called embryos, form and dissolve continually in the undercooled liquid. When an embryo of radius r forms, the free

energy changes by ΔG = −(4/3)πr³ΔGv + 4πr²γ, where γ is the solid-liquid interfacial energy. The first term is a gain proportional to volume, and the second is a cost proportional to surface area. For small r the surface term wins and

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