---
title: "Solidification: nucleation and grain growth"
subject: "Material Science"
chapter: 5
key: "semester_3/material_science:solidification-nucleation-and-grain-growth"
source: https://www.bctengineer.com/q/semester_3/material_science/solidification-nucleation-and-grain-growth
site: BCT Engineering
---

# Solidification: nucleation and grain growth

Material Science · Chapter 5: Solidification, Phase Relations and Strengthening Mechanism

- Asked in: year not given, 8 marks
- Video: [How is the grain structure of metals formed? Solidification/crystallization of melts!](https://www.youtube.com/watch?v=H50zsHuIgrU) — tec-science
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/material_science/solidification-nucleation-and-grain-growth
- Whole chapter: https://www.bctengineer.com/md/semester_3/material_science/chapter-5

## Question

Explain the process of solidification of a pure metal. Describe homogeneous and heterogeneous nucleation, grain growth, dendrite formation and the cooling curve showing undercooling.

## Short answer

Solidification proceeds by nucleation and growth. The cooling curve shows undercooling below Tm, recalescence back to Tm, then constant temperature. Homogeneous nucleation needs large undercooling; heterogenous nucleation on impurities needs small undercooling. Grains grow as dendrites, meeting at boundaries; fast cooling gives fine grains.

## Answer

Solidification is the change of a metal from liquid to solid. It occurs in two steps: **nucleation** of tiny solid particles (nuclei) and **growth** of these nuclei into grains.

#### Cooling curve of a pure metal

```text
 T
 |\
 | \  liquid cools
 |  \
 Tm |---\  /---------------\     <- arrest at Tm (freezing)
 |     \/                  \
 |  undercooling dT,         \   solid cools
 |  then recalescence          \
 +-----------------------------------> time
```

A pure metal freezes at a constant temperature $T_m$. The liquid cools to slightly below $T_m$ (**undercooling** $\Delta T$), nuclei form and release the latent heat of fusion, the temperature rises back to $T_m$ (recalescence), and it stays constant until solidification is complete.

#### Nucleation
- **Homogeneous nucleation**: nuclei form in the pure liquid by random clustering of atoms. A cluster of radius $r$ has a free-energy change $\Delta G = \tfrac43\pi r^3\Delta G_v + 4\pi r^2\gamma$. Only clusters with $r > r^*$ (the critical radius) are stable. A large undercooling is needed.
- **Heterogeneous nucleation**: nuclei form on mould walls, impurities or added inoculants. The surface-energy barrier is lower, so only a small undercooling (0.1-10 K) is needed. This is the usual case in castings; grain refiners (Ti, B in aluminium) exploit it.

#### Grain growth and dendrites
Nuclei grow as atoms attach to them. When the liquid ahead of the interface is undercooled, small protrusions grow into the liquid faster than the flat front, giving a tree-like crystal called a **dendrite** (primary, secondary and tertiary arms). The arms thicken until they meet, and the remaining liquid fills the gaps. Each dendrite becomes one grain, and grains meet at **grain boundaries**.

```text
     |   /|\   dendrite arm
   --+--/-+-\--
     | /  |  \
     |/   |   \
```

#### Effect of cooling rate
Fast cooling gives more nuclei, hence fine grains with higher strength and toughness; slow cooling gives coarse grains.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does temperature rise back to Tm after undercooling?
   A. Heat from furnace
   B. Latent heat of fusion released
   C. Cooling stops
   D. Heat of mixing
   Answer: B. Release of latent heat raises temperature to Tm. (Key point: Recalescence)

2. Why is heterogeneous nucleation more common in castings?
   A. Needs larger undercooling
   B. Occurs only in pure liquid
   C. Surface energy barrier is lower on mould walls and impurities
   D. Produces no grains
   Answer: C. Small undercooling is enough on existing surfaces. (Key point: Heterogeneous nucleation)

3. How do dendrites form?
   A. Flat front growth
   B. Protrusions grow faster into undercooled liquid
   C. From solid state
   D. By melting
   Answer: B. Protrusions in undercooled liquid grow faster, forming tree-like arms. (Key point: Dendrites)

4. Effect of fast cooling?
   A. Fine grains, higher strength
   B. Coarse grains
   C. No nuclei
   D. Lower strength
   Answer: A. More nuclei form, giving fine grains. (Key point: Cooling rate)

## Related in Material Science

- [Cooling of 3% C cast iron](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Ahypoeutectic-cast-iron-3-carbon) — Material Science, chapter 6
- [Critical nucleus radius for copper](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Acritical-nucleus-radius-copper) — Material Science, chapter 5
- [Annealing of cold-worked metals](https://www.bctengineer.com/question.md?key=semester_3%2Fmaterial_science%3Aannealing-recovery-recrystallization-grain-growth) — Material Science, chapter 4

## Related in other subjects

- [Homogeneous/heterogeneous catalysis; intermediate compound theory](https://www.bctengineer.com/question.md?key=semester_2%2Fengineering_chemistry%3Ahomo-hetero-intermediate) — Engineering Chemistry, chapter 2
- [Heterogeneous vs homogeneous; CORBA](https://www.bctengineer.com/question.md?key=semester_7%2Fdistributed_system%3Ahetero-homo-corba) — Distributed System, chapter 4
- [Homogeneous vs heterogeneous applications](https://www.bctengineer.com/question.md?key=semester_7%2Fdistributed_system%3Ahomo-hetero-apps) — Distributed System, chapter 4
- [Solidification, shrinkage and casting defects](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Asolidification-shrinkage-casting-defects) — Manufacturing and Production Processes, chapter 4