Lecture 7
Review of Difficult Topics
MATLS 4L04: Aluminum Section
Driving Force for Solidification
• From thermodynamics,
solidification is
spontaneous when Gs –
GL < 0
• The more negative this
quantity (Gs – GL), the
larger the driving force
for solidification
• What makes this quantity
more negative?
2
Nucleation Activation Energy
• If a system containing liquid is just below the
melting point will it spontaneously solidify?
3
Effect of Temperature
4
Planar Interface Stability –
Superheated Liquid
• Solidification is controlled by the
rate at which latent heat is
conducted away from the
interface
• What happens when a pure
solid with a planar front grows
into a superheated liquid?
5
Planar Interface Stability –
Supercooled Liquid
• What happens when a pure solid
with a planar front grows into a
supercooled liquid?
6
Single Phase - Scheil
Solidification
• No diffusion of solute in the solid
• Perfect mixing in the liquid
• Can lead to cored structures (ie.
solute concentration gradient in
single phase)
• Can also end up with eutectic
forming at the end of solidification
7
Constitutional Supercooling
• Looking at the interface of a steadystate situation
• For pure material non-planar growth
or dendritic/cellular growth, occurs
due to the negative temperature
gradient in the liquid (ie. supercooling)
• Dendritic growth can also occur in an
alloy with a positive temperature
gradient in the liquid, as long as there
is a composition gradient in the liquid
ahead of the interface
8
Solute Hardening
• Dislocations themselves
have strain energy fields
• Dislocations moving
through lattice interact
with strain fields of solute
• This segregation of solute
atoms to dislocations
makes further movement
of the dislocation difficult
as it needs to be “torn”
away from this lower
energy state
Factors that Affect the Solubility
of an Element
• The amount of a solute atom that can be
dissolved in a solution depends on the
similarity of:
1.
2.
3.
4.
Atomic size
Crystal structure
Electronegativity difference
Valence
Effectiveness of Different Solute
Atoms with Al
• In order for a solute to be an effective
strengthener it needs to have a good
combination of:
– Atomic size mismatch
• Leads to larger strain fields
– Solubility
• Leads to more solute atoms present
Solute Strengthening
Effectiveness
Mg
R = 0.160 nm
Al
R = 0.143 nm
Fe
R = 0.124 nm
3 Key Steps To Creating an AgeHardened Alloy
• Step 1: Solutionize
• Step 2: Quench
• Step 3: Age
13
Nucleation in a Solid
• Homogenous
• ∆𝐺 = −𝑉∆𝐺𝑉 + 𝐴𝛾 + 𝑉∆𝐺𝑠
•
𝑟∗
•
∆𝐺 ∗
=
2𝛾
∆𝐺𝑉 −∆𝐺𝑠
=
16𝜋𝛾 3
3 ∆𝐺𝑉 −∆𝐺𝑠 2
14
Aside on Coherency
• Interfaces can either be:
– Coherent
– Semi-coherent
– Incoherent
Coherent
Semi-coherent
Coherency Strains
Incoherent
15
Particle Growth
• Equate flux of solute into the
particle
v(Cβ-Ce)
• To the flux of solute from far
away to the interface
-D(Cβ-C0)/√(Dt)
• Gives a growth rate of x = kt1/2
• When particles continue to
grow and their diffusion
gradients overlap x=kt1/3
• Also, coherency of interface
can effect growth in certain
directions
16
Precipitate Evolution
• Why does it bother
with the
intermediate phases?
• Nucleation of a phase
is dictate by the
activation energy
16 3
G* 
3(GV  GS ) 2
17
18
Solvuses
19
Coherency Strain Hardening
• Similar to a solute atom, a
particle will cause some
coherency strains due to the
elastic size mismatch
between the particle and the
parent lattice atoms
• A dislocation will be slowed
down by the coherency
strains surrounding a particle
Chemical Surface Hardening
• When a dislocation travels through a particle it
must create additional particle/matrix interfacial
area
• Larger stress (strengthening) required to shear
particle and increase interfacial energy
Gleiter and Hornbogen (1965)
Orowan Bowing
• If you try and push a
dislocation between two
particles it will bend
resulting in a dislocation
with a certain curvature
• The shear stress (τ) required
to push a dislocation
between two particles such
that it reaches a curvature
represented by a diameter
(d) is given by:
• 𝜏=
𝐺𝑏
𝑑
Orowan Bowing
• If the stress is reached
that bows the dislocation
to a diameter equal to
the spacing between
particles the dislocation
can break free from the
particles with a small
increase in stress
• 𝜏𝑦 =
𝐺𝑏
𝐿
Strengthening Effect
Mechanisms of Strengthening with Time
1. Solute strengthening
2. Coherency Strain Hardening
3. Chemical Surface Hardening
4. Orowan Bowing
Softening vs. Strengthening
• It is not uncommon that Aluminum alloys need to undergo a
softening process
– Ex. Softening a cold-rolled sample between passes to allow for further
deformation
– Softening will decrease strength and increase ductility
• Most of the strengthening techniques used for Aluminum alloys
have an associated softening technique
Strengthening Technique
Softening Technique
Age hardening
Solution heat treatment
Overageing (undesirable)
Grain refinement
Grain growth
Work hardening
Recovery, recrystallization,
Solute hardening
None
25
Particle Coarsening / Oswald
Ripening
• Solubility of solute in the
matrix near small
precipitates is higher than
that of large precipitates
• Results in a concentration
gradient in the matrix
leading to transfer of
solute from small particles
to large particles
• Large particles grow while
small particles dissolve
26
Recovery
• Lowers the energy of a deformed material by:
– Annihilation of dislocations
• Dislocations of opposite signs move through the material
until they can cancel one another
– Spatial rearrangement of dislocations
• Dislocations are arranged such that they are in an
arrangement that is lower in energy
• This new arrangement minimizes the interaction of similar
strain fields between dislocations
• Note: Recovery does not change the shape of
grains just the dislocation structure
27
Recovery Kinetics
• In order to increase the rate at which recovery
occurs
– Increase the temperature
– Increase the level of stress
– Reduce the solute content
– Reduce the presence of second phase particles
28
Recrystallization
• Nucleation and
growth of strain
(dislocation) free
grains consuming
deformed or
recovered material
• Mechanism of Strain
Induced Boundary
Migration (SIBM)
Grain II
Grain I
Grain II
Grain I
nucleus
29
Solute Drag
• If there is significant solubility of solute in
aluminum or the material is being heated in the
single phase region and the solute is present in
solution, then it can slow down recrystallization
kinetics through the mechanism of solute drag
• Solute atoms tend to be in lower energy states at
grain boundaries and will often segregate there
• During recrystallization when these boundaries
are trying to move, they are slowed by the solute
as the boundary mobility is dependent on solute
diffusion
30
Grain Boundary Pinning / Zener
Drag
• A dispersion of particles creates a pinning
pressure that will oppose the pressure that
drives the movement of the grain boundary
during recrystallization
• Pinning force of one particle is
F = πrγ
• There are N particles per unit volume
3𝑓𝑣
𝑁=
4𝜋𝑟 3
• The number of particles that will intersect with
the grain boundary is
3𝑓𝑣
𝑁𝑖𝑛𝑡 = 2𝑟𝑁 =
2𝜋𝑟 2
• The Zener pinning pressure per unit area is
3𝑓𝑣
3𝑓𝑣 γ
𝑃𝑧 = 𝐹𝑁𝑖𝑛𝑡 = πrγ
=
2𝜋𝑟 2
2𝑟
31
Recovery vs Recrystallization
Recovery
• Partial recovery of
properties
• Microstructure of
rearranged dislocations
• Structure of grains related
to the deformed grains
• Some reduction in strength
and increase in ductility
Recrystallization
• Complete recovery of
properties
• Microstructure with much
fewer dislocations
• New grains formed with no
relation to old structure
• Much softer and more
ductile
32
Grain Growth
• Grain boundaries are regions of disorder and
therefore increase the energy of a material
• Therefore, there is a driving force to reduce the
number of grain boundaries in order to lower the
energy
• This manifests itself in the process of grain
growth
• As grain growth requires the movement of grain
boundaries, this is a thermally activated process
33
Marking Rubric on Lab Report
Students will obtain 70 % Marks of the lab report part (50 marks) as long as
submitting the report before due day. The marking rubric for the remaining
30% depends on the report quality including
 Objective and Background information 10
 Procedure 20
 Result and discussion 40
 Conclusion
10
 References (at least 10 references) 10
 Format 10