MECE 3345 Materials Science
20-Phase Transformations 1
Jae-Hyun Ryou
Department of Mechanical Engineering
Cullen College of Engineering
University of Houston
Introduction
• Objectives
– Learn on basics of phase transformations
• Lecture consists of
– Types of phase transformations
– Thermodynamics of phase transformation
– Kinetics of phase transformation
– Metastable states
2
Phase Transformations:
Introduction
• Phase change and more
• Very important in material processing
– Microstructure alteration
– Material property control
• Mechanical property (strength, hardness, ductility, etc.)
Other phases
3
Types of Phase Transformations
• Simple phase change
– No change in # of phase or composition
– Pure elements
– Solidification of pure metal, allotropic phase
transformation (polymorphic transformation)
• Diffusional transformation
– Often involving different phase w/ different composition
– Precipitate
– Eutectic, eutectoid reaction
• Diffusionless transformation
– Final product: metastable phase
– Important in steel processing
4
Steps of Phase Transformations
• Nucleation
– Nuclei (seeds) act as
templates on which crystals
grow
– Driving force (ΔG) to nucleate
increases w/ increasing ∆T
(supercooling)
• Lower temperature in case of
cooling (solidification, etc.)
– Some embryos do not go
through nucleation and growth
• Growth
– Once nucleated, growth
proceeds until equilibrium is
attained
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Types of Nucleation
• Homogeneous nucleation
– Nuclei form in the bulk of liquid
metal
– Requires considerable
supercooling
(typically 80-300 °C)
• Heterogeneous nucleation
– Nucleation on heterogeneous
surface
– Much easier since stable
“nucleating surface” is already
present — e.g., mold wall,
impurities in liquid phase
– Only very slight supercooling
(0.1-10ºC)
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Thermodynamics of Homogeneous
Nucleation I
• Nucleus size (r) ↑
– Volume free energy ↓
(more negative w/ r)
– Surface energy ↑
(more positive w/ r)
∆𝐺𝐺 = −43𝜋𝜋𝑟𝑟 3 ∆𝐺𝐺𝑉𝑉 + 4𝜋𝜋𝑟𝑟 2 𝛾𝛾
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Thermodynamics of Homogeneous
Nucleation II
Surface Free Energy - destabilizes
the nuclei (it takes energy to make
an interface)
∆GS = 4πr 2 γ
γ = surface tension
∆GT = Total Free Energy
= ∆GS + ∆GV
Volume (Bulk) Free Energy –
stabilizes the nuclei (releases energy)
4 3
∆GV = πr ∆Gυ
3
∆Gυ =
volume free energy
unit volume
8
r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy)
Thermodynamics of Homogeneous
Nucleation III
• Critical radius for homogeneous nucleation
− 2γTm
r* =
∆Hf ∆T
r* = critical radius
γ = surface free energy
Tm = melting temperature
∆Hf = latent heat of solidification
∆T = Tm - T = supercooling
∴
r*
decreases as ∆T increases
For typical ∆T
r* ~ 10 nm
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Kinetics of Nucleation
• More supercooling (low T)
– Good in terms of thermodynamics (smaller r*)
– Slow in diffusion (less chance of attachment to nuclei)
• Highest nucleation at moderate supercooling
10
Growth Rate and Overall
Transformation Rate
• Kinetics of growth
(after nucleation)
– Growth rate
• Mostly dependent
on diffusion of
atoms
𝑄𝑄
– 𝐺𝐺̇ = 𝐶𝐶 exp(−𝑘𝑘𝑘𝑘
)
• Transformation
rate
– Nucleation rate
and growth rate
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Kinetics of Phase Transformation I
• Kinetics of phase
transformation
– Time taking for
transformation
– Rate ↑ ⇒ time for
transformation ↓
12
Kinetics of Phase Transformation II
• Kinetics of phase transformation
– Time taking for transformation
– Rate ↑ ⇒ time for transformation ↓
13
Fraction transformed, y
Kinetics of Phase Transformation III
transformation complete
Fixed T
maximum rate reached – now amount
unconverted decreases so rate slows
0.5
t0.5
rate increases as surface area increases
& nuclei grow
log t
Avrami equation => y = 1- exp (-kt n)
fraction
transformed
time
– k & n are transformation specific parameters
By convention
rate = 1 / t0.5
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Kinetics of Recrystallization
135°C 119°C
1
113°C 102°C
10
88°C
102
43°C
104
• For the recrystallization of Cu, since
rate = 1/t0.5
rate increases with increasing temperature
15
Metastable Phase
• Equilibrium phase
– Most thermodynamically stable
– But takes time to reach
– If not enough time allowed, often
metastable phase formed
• Metastable phase
– Not the most thermodynamically stable
– But practically existing (extremely slow
kinetics)
– Often very important in engineering
materials
16
Superman and Diamond
• Adventures of Superman
– TV series (1951-1957) Episode Guide
104 episodes, and one public service show
– Episode #40 "Jungle Devil"(1953)
• Superman creates a diamond by compressing a piece
of coal (carbon atoms) with his hand.
http://www.supermanhomepage.com/tv/tv.php?topic=episodeguides/t-aos
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Summary
• Important concepts
– Steps of phase transformations
– Conditions for nucleation of phase
transformation
– Kinetics of phase transformation as a function of
temperature
• Homework assignments
– HW #3 Q13-14, 16
18
Further Reading
• W. D. Callister and D. G. Rethwisch, Materials
Science and Engineering An Introduction
– Chapter 10. Phase Transformations
•
•
•
•
10.1 Introduction
10.2 Basic concepts
10.3 The kinetics of phase transformations
10.4 Metastable versus equilibrium states
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