ENMAT101A Engineering Materials and Processes
Associate Degree of Applied Engineering
(Renewable Energy Technologies)
Lecture 9 – Equilibrium diagrams
www.highered.tafensw.edu.au
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Equilibrium diagrams
Reference Text
Section
Higgins RA & Bolton, 2010. Materials for Engineers and Technicians,
5th ed, Butterworth Heinemann
Ch 9
Additional Readings
Section
Callister, W. Jr. and Rethwisch, D., 2010, Materials Science and
Engineering: An Introduction, 8th Ed, Wiley, New York.
Ch 10
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Equilibrium diagrams
Note: This lecture closely follows text (Higgins Ch9)
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Equilibrium diagrams
An equilibrium diagram (or phase diagram) is a graphical
method of illustrating the relationship between the
composition, temperature, and structure, or state, of any alloy
in a series.
“Series” might be iron/carbon, lead/tin, copper/zinc, where the diagram is
plotted over a range of percentage mixtures.
The diagram can help us to decide suitable heat-treatment processes for a
particular carbon-steel. For a non-ferrous alloy system, the equilibrium
diagram will often give us a pretty good indication of the structure - and
hence the mechanical properties.
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The Iron-Carbon equilibrium
diagram over a very small
range of Carbon (0 to 2% by
weight, or 0 to 7% by atoms)
This is as much carbon as
steel can handle before it
turns into cast iron, and then
useless rock.
This diagram will meet you
again soon (not today).
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Obtaining equilibrium diagrams (Higgins 9.2)
How are equilibrium diagrams obtained?
Even for a simple binary alloy, some poor person had to carefully study
each percentage just to plot a single dot on the curve!
There are about 70 metals, so that would mean 2415 combinations!
Not quite – some don’t mix – e.g. high melting-point tungsten with very
reactive caesium.
However, lots of metallic elements have been successfully alloyed with
each other and with some of the non-metallic elements like carbon, silicon
and boron.
There are a lot of alloys!
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Melting / Boiling of Elements
www.ptable.com
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Lead-tin alloys (Higgins 9.2.1)
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Gas to Liquid. (Metal Vapour Condensing)
The temperature of a metal vapour (gas) falls until it reaches the boiling
point where it starts to turn into liquid (condense).
In a liquid the atoms are randomly mixed together and are free to slide
around. The atoms are held together only by weak forces of attraction at
this stage, the liquid lacks cohesion and will flow.
Gas Animations: Tim Lovett 2012
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Latent Heat
A pure metal solidifies at a fixed
temperature (melting point).
The liquid resists cooling below the
melting point until the liquid has
solidified. This requires removal of
the Latent Heat. This energy is
called the latent heat of fusion
(solidification in this case).
Alloys (metal mixtures) can have a
range of melting temperatures.
Higgins: Fig 4.1
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Lead-tin alloys (Higgins 9.2.1)
Other ratios are tested for mushy and freezing points.
They must be cooled slowly (to keep in EQUILIBRIUM)
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Lead-tin alloys (Higgins 9.2.1)
Plotting the
data on a
composition
axis vs
temperature.
This is the
beginning of an
equilibrium
diagram.
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Lead-tin alloys (Higgins 9.2.1)
This is the whole
thing for Lead and
Tin.
http://www.ami.ac.uk/courses/topics/0244_tsm/index.htm
l
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Types of equilibrium diagrams (Higgins 9.3)
A useful alloy must be soluble when molten, or there is no chance of any
solid mixture. (E.g. Molten lead with zinc floating on top).
In the solid state the metals may be;
1. Completely soluble.
2. Completely insoluble.
3. Partially soluble.
To stay in equilibrium, some alloys need to be cooled extremely slowly –
way too slowly for many industrial situations.
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Two metals fully soluble (Higgins 9.3.1)
Above the liquidus,
mixture is liquid.
Below the solidus,
mixture is solid.
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Two metals fully soluble (Higgins 9.3.1)
Follow notes in Higgins 9.3.1 in detail
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Two metals completely insoluble (Higgins 9.3.2)
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Dendritic solidification (Higgins 4.3.1)
As the molten pure metal cools below its freezing point,
crystallisation will begin.
It starts out with a single unit – (e.g. BCC for Tungsten).
New atoms will join the 'seed crystal' and grow onto the
structure much like a snowflake (except the metal is
forming in liquid, not a cloud of droplets).
The branched
crystal is called a
'dendrite‘ (Greek
for tree).
BCC Unit: Higgins Fig 4.3
Snowflake: Wikipedia
Higgins Fig 4.4
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Dendrite of Silver: Wikipedia
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Two metals completely insoluble (Higgins 9.3.2)
Above the liquidus,
mixture is liquid.
Below the solidus,
mixture is solid.
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Two metals completely insoluble (Higgins 9.3.2)
Follow notes in Higgins 9.3.2 in detail
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Two metals are partially soluble (Higgins 9.3.3)
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Two metals completely insoluble (Higgins 9.3.3)
Follow notes in Higgins 9.3.3 in detail
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Precipitation from a solid solution (Higgins 9.4.2)
Follow notes in
Higgins 9.4 in
detail
At higher temperature,
water can dissolve
more salt.
Likewise, at higher
temperature, metal A
can dissolve more
metal B
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Precipitation from a solid solution (Higgins 9.4)
Follow notes in
Higgins 9.4.2 in
detail
Copper solute in
Aluminium (Cu/Al diagram)
Fast cooling (quenching)
prevents precipitate forming.
Age hardening allows
precipitate to attempt to form
is solid – causing lattice
distortion > hindering slip >
hardening the alloy. E.g.
Duralumin 4%Cu.
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Ternary equilibrium. (Higgins 9.5)
Three metals, a 3D diagram!
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Online Properties Resources.
Teach yourself phase diagrams
Handout
http://www-g.eng.cam.ac.uk/mmg/teaching/phasediagrams/i2a.html
Wikipedia: Materials properties
Metal Grains and processing
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GLOSSARY
Phase Diagram
Equilibrium Diagram
Liquidus line
Solidus line
Coring or cored structure
Dendritic
Binary
Tertiary
Solid phase change
Eutectic
Phase
Eutectic phase
Hypereutectoid alloy
Hypoeutectoid alloy
Solubility limit
System
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QUESTIONS
Callister: Ch3 (Mostly about calculating atomic packing factors - too esoteric)
Moodle XML: Some questions in 10102 Classification and 10105 Steel
1. Define all the glossary terms.
2. There are two names for the same thing: Phase Diagram and Equilibrium
Diagram. Both make sense. Describe what phase and equilibrium refer to.
3. Why would it be difficult to make an alloy of Rhenium and Cadmium?
4. Why is it important for a eutectic mixture to cool slowly during the creation of an
equilibrium diagram?
5. What happens between the liquidus and solidus lines of a simple binary
equilibrium diagram with complete solubility?
6. In the Cadmium-Bismuth thermal equilibrium diagram, What happens as a
mixture that crosses the BE line, the AE line, the EC line, the ED line?
7. In the lead-tin thermal equilibrium diagram, what does a and b stand for? What
is the difference between Lead, Tin, a and b? What happens as a mixture that
crosses the AB line, the CB line, the BE line, the EF line?
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