MATS1192-材料学代写
时间:2023-03-03
Module 2, Lecture 2
Phase diagrams and phase transformations
MATS1192 Design and Applications of Materials in Science and
Engineering
A/Prof. Judy Hart
School of Materials Science and Engineering, UNSW Sydney
Office: 339, Hilmer Building
j.hart@unsw.edu.au
MATS1192 2023 1 / 48
Outline of the course
Week Monday Thursday
1 1. Atomic bonding 1. Atomic packing
2 1. Defects/WHS 2. Diffusion/Structure of metals*
3 2. Phase diagrams* 3. Elastic Deformation
4 3. Plastic Deformation/ 3. Introduction to
Dislocations* Fast Fracture/Ethics
5 3. Strengthening mechanisms*/ 3. Fast Fracture*
Revision
6 Revision Site visit
7 4. Steels* Industry guest lecture
8 4. Non-ferrous alloys 5. Polymers
9 PUBLIC HOLIDAY Site visit
10 5. Ceramics 5. Composites
Conference – Week 10
* Online tutorial must be completed before class
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Today
1 Review of the previous lecture and online tutorial
2 Phase transformations
Determining phase composition and amounts
Microstructure development
Equilibrium and non-equilibrium
3 Review
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Things to do...
You have been put into groups for the group assignment – Check
which group you are in
Contact your group for the group assignment
Let me know if there is a particular member of staff you would like to
interview for the group assignment
Sign up for camp (if you can’t/don’t want to go, there will be an
alternative assessment – let me know)
Complete Tutorial 3B on Plastic Deformation before next Monday’s
class
Assessed quiz for Module 2 will be open from Monday, Week 4, 12pm
(mid-day), to Tuesday, Week 4, 11:59pm
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Labs
First lab (Energy Materials) is this week for most groups (next week for
one group).
All labs are held in the Hilmer building (E10), Room G12.
DON’T BE LATE!
Lab worksheets are available on Moodle.
Lab reports are due one week after the lab. Reports should be submitted
in electronic format on Moodle.
You must attend the lab at the time you signed up for
Labs are in person – if you can’t make it on the day (e.g. unwell),
apply for Special Consideration and contact Caitlin, she will arrange a
make-up lab
Bring lab coat and safety glasses, wear enclosed shoes – otherwise,
you will not be allowed in the lab!
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Group assignment – Interview with an academic
UNSW is a research-intensive university.
What is the benefit to you of coming to study at a research-intensive
university?
How is being at a research-intensive university different from being a
school student?
You will work in groups to interview a member of staff in the School of
Materials Science and Engineering, to learn about their research.
Interviews will start in Week 6. Report (individual) is due at the end of
Week 8.
This assignment will also allow you to develop team-work and
communication skills, particularly professional communication.
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Reference
Engineering Materials 2, 4th Edition, M.F. Ashby and D.R. Jones –
Chapters 3 and 4
Materials Science and Engineering: An Introduction, Australia & New
Zealand Edition, W.D. Callister and D.G. Rethwisch – Chapter 9
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Objectives
Use binary metal alloy phase diagrams to find the phases present
under given conditions and their compositions, and also apply the
Lever Rule to find the amounts of phases present
Identify liquidus and solidus lines, as well as isotherms, on a phase
diagram
Define the term eutectic, identify the eutectic point on a phase
diagram and give the reaction that occurs on cooling through the
eutectic point
Describe the phase transformations that woud be expected to occur,
and the microstructure expected to develop, when an alloy is cooled
Explain the difference between equilibrium and non-equilibrium
conditions, and how cooling rapidly may result in different phases
present from those expected from the phase diagram
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Interactive slides
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Review MATS1192 2023 9 / 48
Five-minute test
1 What’s the difference between an interstitial solid solution and a
substitutional solid solution? Under what conditions would you expect
each to form?
In an interstitial solid solution, the solute atoms fit into the spaces
between the solvent atoms. In an substitutional solid solution, the
solute atoms replace solvent atoms. Interstitial solid solutions form
when the solute atoms are small. Substitutional solid solutions form
when the solute and solvent atoms are similar size.
2 What might occur when we add an alloying element to a metal at a
concentration above the solubility limit?
Formation of a second solid solution, or formation of a chemical
compound
Review MATS1192 2023 10 / 48
Constitution and structure of a metal alloy
To describe an alloy and predict/understand its properties, we need to
know:
1 the overall (average) composition
2 the number and type of phases present
3 the amounts of each phase
4 the composition of each phase (i.e. solid solutions can have different
compositions)
We can find all of these using the phase diagram for the alloy.
The properties of a metal alloy also depend strongly on the microstructure:
1 grain size and shape of each phase
2 distribution of the phases
With this information, we can understand the properties and behaviour of
metal alloys.
Review MATS1192 2023 11 / 48
Phase diagram – Binary alloys
Phase diagrams show the phase(s) that will be present at equilibrium
under particular conditions.
We will look at phase diagrams for binary alloys that:
have complete solid solubility (last week and online Tutorial 2B)
form two solid solutions with different compositions (online Tutorial
2B and today)
form a chemical compound in a solid solution (online Tutorial 2B and
today)
For alloys with more than two components, phase diagrams can become
very complicated.
Review MATS1192 2023 12 / 48
Five-minute test
1 Sketch a typical phase diagram for a binary alloy with complete solid
solubility.
2 What is the definition of phase transformation?
Definition
Phase transformation – A change in the number or type of the phases
present in the microstructure of a material, caused by a change in
conditions (e.g. temperature).
3 What is an example of a phase transformation?
Review MATS1192 2023 13 / 48
Binary eutectic alloy
Pb-Sn is an example of a binary eutectic alloy.
Review MATS1192 2023 14 / 48
Practice
Pb-Sn is an example of a binary eutectic alloy.
If a Pb-40wt% Sn alloy is
heated from room
temperature:
1 At what temperature
does a liquid first
form?
183 ◦C
2 At what temperature is
melting complete?
∼ 235 ◦C
3 How many phases are
present at
(a) 320 ◦C
1
(b) 210 ◦C
2
(c) 140 ◦C
2
Review MATS1192 2023 15 / 48
Practice
Pb-Sn is an example of a binary eutectic alloy.
1 One of the phase
boundaries is an
isotherm – which one?
2 Where is the eutectic
point?
3 What phase
transformation occurs
at the eutectic point on
cooling?
Review MATS1192 2023 16 / 48
Phase diagram – Intermediate phases
In some alloys, an intermediate chemical compound forms, such as Mg2Pb
in Mg-Pb alloys.
These compounds have
fixed composition –
they appear as a
vertical line on the
phase diagram.
Review MATS1192 2023 17 / 48
Diffusion
Phase transformations usually require diffusion.
Definition
Diffusion – A process of random movement of atoms/molecules that takes
a system towards an equilibrium state.
Diffusion is time-dependent and temperature-dependent.
Phase transformations MATS1192 2023 18 / 48
Nucleation and Growth
Phase transformations usually require diffusion and occur by a process of
nucleation and growth.
Definitions
Nucleation – The formation of very small particles (nuclei) of the new
phase.
Growth – The nuclei increase in size until the phase transformation is
complete.
Phase transformations MATS1192 2023 19 / 48
Microstructure
The final microstructure of a material will depend on the phase
transformations that occur (which we can predict from the phase diagram)
and how they occur, e.g. the heating and cooling rates.
Definition
Microstructure – The structural features of a material at the microscopic
scale. For metal alloys, this means, for example, the size and shape of the
grains, and the distribution of the phases, if more than one phase is
present.
Definition
Microstructure development – How the microstructure changes when the
material is heated or cooled.
The final microstructure has a strong influence on the properties.
Phase transformations MATS1192 2023 20 / 48
Microstructure development – Alloy with complete solid
solubility
For alloys, solidification
(usually) takes place over
a range of temperatures.
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Determining phase composition
Whenever there are two phases present in a material, they will often have
different compositions.
Phase transformations Phase composition and amounts MATS1192 2023 22 / 48
Determining phase composition
In a two-phase field on a phase diagram, we can calculate the composition
of the two phases.
1 Locate the point on
the phase diagram of
interest (labelled B)
2 Draw a tie line – a
horizontal line that
intersects with the
phase boundaries
3 The composition at
the points where the
tie line intersects with
the phase boundaries
give the compositions
of the two phases
Phase transformations Phase composition and amounts MATS1192 2023 23 / 48
Microstructure development – Alloy with complete solid
solubility
When there are two phases present,
they will have different compositions.
Nickel has a higher melting
temperature than copper. When a
Cu-Ni alloy first starts to solidify, the
nickel prefers to solidify first, so the
initial solid that forms has more Ni
than the average amount.
If there is more Ni in the solid phase,
there must be less nickel in the liquid
phase.
Phase transformations Phase composition and amounts MATS1192 2023 24 / 48
Microstructure development – Alloy with complete solid
solubility
As cooling continues and more solid
forms, more Cu starts to go into the
solid phase – the Ni content of the
solid phase gradually decreases.
The last bit of liquid to solidify has a
very low Ni content.
Phase transformations Phase composition and amounts MATS1192 2023 25 / 48
Determining amount of each phase – the Lever Rule
1 Locate the point on
the phase diagram of
interest (labelled B)
2 Draw a tie line – a
horizontal line that
intersects with the
phase boundaries
Phase transformations Phase composition and amounts MATS1192 2023 26 / 48
Determining amount of each phase – the Lever Rule
3 The fraction (by mass)
of one phase is the
length of the tie line
from the point of
interest to the phase
boundary for the other
phase divided by the
total length of the tie
line.
WL =
S
R+ S
=
Cα − C0
Cα − CL
Wα =
R
R+ S
=
C0 − CL
Cα − CL
Phase transformations Phase composition and amounts MATS1192 2023 27 / 48
Lever Rule – Practice
At the point labelled ’c’, calculate
the proportion (by mass) of the alloy
that is in the solid phase, and the
proportion in the liquid phase.
Wα =
3
11
= 27%
Wliquid =
8
11
= 73%
Phase transformations Phase composition and amounts MATS1192 2023 28 / 48
Microstructure development – Binary eutectic alloy
For a binary eutectic alloy, the phase transformations that occur are
different for different compositions.
Phase transformations Microstructure development MATS1192 2023 29 / 48
Microstructure development – Pb-rich composition
Phase transformations Microstructure development MATS1192 2023 30 / 48
Microstructure development – Eutectic composition
How many phases are present at 250 ◦C?
1
What is the composition of the phase(s) present at 250 ◦C?
61.9wt% Sn
Phase transformations Microstructure development MATS1192 2023 31 / 48
Microstructure development – Eutectic composition
How many phases are present at 180 ◦C?
2
What is the composition of the phase(s) present at 180 ◦C?
α is ∼18wt%
Sn, β is ∼98wt% Sn
Phase transformations Microstructure development MATS1192 2023 32 / 48
Microstructure development – Eutectic composition
As the phase transformation proceeds, redistribution of tin and lead occurs
by diffusion at the interface between the solid and liquid.
Phase transformations Microstructure development MATS1192 2023 33 / 48
Microstructure development – Eutectic composition
The microstructure of a Pb-Sn alloy of eutectic composition consists of
alternating layers of a lead-rich solid solution (dark) and a tin-rich solid
solution (light).
Phase transformations Microstructure development MATS1192 2023 34 / 48
Microstructure development – Off-eutectic composition
For an Pb-40 wt%Sn alloy: 1 What is the first solid phase to
form as it is cooled from the
liquid state?
α
2 What phase(s) are present at
220 ◦C (the point labelled k)?
Find the composition of the
phases at this temperature.
3 What happens to the
composition of the remaining
liquid as the temperature
decreases? What is the
composition of the liquid phase
when the eutectic temperature
is reached (the point labelled l)?
Phase transformations Microstructure development MATS1192 2023 35 / 48
Microstructure development – Off-eutectic composition
For an Pb-40 wt%Sn alloy:
How many phases are present
at room temperature?
2
There are two types of α
phase present in the
microstructure – α phase that
formed before the eutectic
temperature was reached,
and layers of α phase in the
eutectic structure (formed at
the eutectic temperature).
The α phase that forms before the eutectic temperature is reached is
called primary α phase.
Phase transformations Microstructure development MATS1192 2023 38 / 48
Microstructure development – Off-eutectic composition
Phase transformations Microstructure development MATS1192 2023 39 / 48
Phase transformations
In these examples of phase transformations, how is the (1) number, (2)
type and (3) composition of the phases present changing?
Melting of a pure metal
No change in the number or composition of the phases present,
change in the type of phase (solid to liquid)
The eutectic reaction – Transformation of a liquid alloy to two solid
solutions on cooling
Change in the number of phases from 1 to 2; change in type of
phases from liquid to solid; change in composition of phases
Transformation of one solid solution to two solid solutions
Change in the number of phases from 1 to 2; no change in type of
phases; change in composition of phases
Phase transformations Microstructure development MATS1192 2023 40 / 48
Practice
For an Al-Si alloy: What is the maximum solid
solubility of aluminium in silicon?
0%
What is the eutectic composition
and temperature?
11.3% Si, 577 ◦C
What phases are present for an
Al-50% alloy at (a) 1200 ◦C, (b)
800 ◦C, and (c) 500 ◦C?
(a) Liquid,
(b) Liquid and pure silicon, (c)
Aluminium-rich solid solution and
pure silicon
What is the composition of the
phases at each of these
temperatures?
(a) 50% Si, (b) 27%
Si and 100% Si, (c) ∼ 1% and
100% Si
Phase transformations Microstructure development MATS1192 2023 41 / 48
Equilibrium and non-equilibrium
1 What is the definition of equilibrium conditions?
A stable state of a system for which the characteristics and properties
do not change with time; a state in which free energy is minimised.
2 Do phase diagrams show us what is happening under equilibrium or
non-equilibrium conditions?
Equilibrium
Phase transformations Equilibrium MATS1192 2023 42 / 48
Non-equilibrium cooling
1 For an Al-4wt%Cu
alloy, what phase(s) is
present at 550 ◦C
under equilibrium
conditions?
α
2 What happens if it is
cooled very slowly
(under equilibrium
conditions) to room
temperature?
θ phase
forms
3 At 300 ◦C, what are the amounts and compositions of the phases
present?
α is ∼ 1wt% Cu; θ is ∼ 53wt% Cu; ∼ 94wt% of the alloy is
in the α phase.
Phase transformations Equilibrium MATS1192 2023 43 / 48
Non-equilibrium cooling
2 What happens if it is
cooled very slowly
(under equilibrium
conditions) to room
temperature?
θ phase
forms
Particles of a second solid phase that form out of an initially uniform solid
phase during cooling are called precipitate particles.
Phase transformations Equilibrium MATS1192 2023 44 / 48
Non-equilibrium cooling
1 What is required
in order for the
phase
transformation to
occur?
Diffusion
2 What do you
think happens if
it is cooled very
quickly from
550 ◦C to room
temperature?
Phase transformations Equilibrium MATS1192 2023 45 / 48
Non-equilibrium cooling
If materials are cooled very quickly, there is often not time for formation of
the equilibrium phases.
The material is then in a non-equilibrium state.
For example, if a Al-4%Cu alloy is cooled quickly, the phase
transformation cannot occur as there is insufficient time for atomic
diffusion. The alloy is in a non-equilibrium state and the microstructure
consists of a super-saturated solid solution.
Definition
Quenching – Cooling a material very rapidly (e.g. by dropping it into cold
water).
Phase transformations Equilibrium MATS1192 2023 46 / 48
Further learning
Read the Course Notes on Phase Diagrams on Moodle
Read Chapters 5 and 10 of Engineering Materials 2, 4th Edition, M.F.
Ashby and D.R. Jones (Case Studies)
Review MATS1192 2023 47 / 48
Revision activity – self-test
Define phase diagram, microstructure and eutectic
Sketch the phase diagrams for alloys with complete solid solubility
and binary eutectic alloys
Explain how the microstructure of a Cu-Ni alloy and a Pb-Sn alloy
develops as it is cooled for different compositions
List some factors that are important in determining the
microstructure of a metal alloy
Explain why the microstructure of metals and metal alloys that have
been rapidly cooled can be different from those that have been cooled
slowly
Review MATS1192 2023 48 / 48


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