1. Engineering Materials and Processes Lecture 9 – Equilibrium diagrams
Prescribed Text:
Ref 1: Higgins RA & Bolton, Materials for Engineers and Technicians, 5th edition, Butterworth Heinemann. ISBN:
Readings:
Callister: Callister, W. Jr. and Rethwisch, D., 2010, Materials Science and Engineering: An Introduction, 8th Edition, Wiley, New York. ISBN
Ashby 1: Ashby, M. & Jones, D., 2011, Engineering Materials 1: An Introduction to Properties, Applications and Design, 4th edition, Butterworth-Heinemann, Oxford UK. IBSN:
Ashby 2: Ashby, M. & Jones, D., 2011, Engineering Materials 2: An Introduction to Microstructures and Processing, 4th edition, Butterworth-Heinemann, Oxford UK. IBSN:
Lecture (2 hrs):
Ref 1, Ch 1: Engineering materials;
Ref 1 Ch 2: Properties of materials.
Laboratory 1 (2 hrs): Hardness test
Callister: Ch 1, 2, 18-21
Ashby 1: Ch 1, 2
Ashby 2: Ch 1 1

2. Equilibrium diagrams Reference Text Section
Higgins RA & Bolton, 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
Engineering Materials and Processes

3. Note: This lecture closely follows text (Higgins Ch9)
Equilibrium diagrams
Note: This lecture closely follows text (Higgins Ch9)
Engineering Materials and Processes

4. 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.
Engineering Materials and Processes

5. This diagram will meet you again soon (not today).
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).
Engineering Materials and Processes

6. 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!
Engineering Materials and Processes

7. Melting / Boiling of Elements
Lots of metal elements.
There are about 70 metals, so that would mean 2415 combinations!
Not really – some don’t mix – e.g. high melting-point tungsten with very reactive caesium.
Engineering Materials and Processes

8. Lead-tin alloys (Higgins 9.2.1)
Engineering Materials and Processes

9. 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.
Higgins RA & Bolton, Materials for Engineers and Technicians, 5th edition, Butterworth Heinemann. Ch 1.2.1
Gas Animations: Tim Lovett 2012
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10. 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
Higgins RA & Bolton, Materials for Engineers and Technicians, 5th edition, Butterworth Heinemann. Ch 4
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11. 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)
Engineering Materials and Processes

12. Lead-tin alloys (Higgins 9.2.1)
Plotting the data on a composition axis vs temperature.
This is the beginning of an equilibrium diagram.
Engineering Materials and Processes

13. Lead-tin alloys (Higgins 9.2.1)
This is the whole thing for Lead and Tin. l
Engineering Materials and Processes

14. 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;
Completely soluble.
Completely insoluble.
Partially soluble.
To stay in equilibrium, some alloys need to be cooled extremely slowly – way too slowly for many industrial situations.
Engineering Materials and Processes

15. Two metals fully soluble (Higgins 9.3.1)
Above the liquidus, mixture is liquid.
Below the solidus, mixture is solid.
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16. Two metals fully soluble (Higgins 9.3.1)
Follow notes in Higgins in detail
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17. Two metals completely insoluble (Higgins 9.3.2)
Engineering Materials and Processes

18. 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).
BCC Unit: Higgins Fig 4.3
The branched crystal is called a 'dendrite‘ (Greek for tree).
Snowflake: Wikipedia
Higgins RA & Bolton, Materials for Engineers and Technicians, 5th edition, Butterworth Heinemann. Ch 4
Higgins Fig 4.4
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19. Dendrite of Silver: Wikipedia
Engineering Materials and Processes

20. Two metals completely insoluble (Higgins 9.3.2)
Above the liquidus, mixture is liquid.
Below the solidus, mixture is solid.
Engineering Materials and Processes

21. Two metals completely insoluble (Higgins 9.3.2)
Follow notes in Higgins in detail
Engineering Materials and Processes

22. Two metals are partially soluble (Higgins 9.3.3)
Engineering Materials and Processes

23. Two metals completely insoluble (Higgins 9.3.3)
Follow notes in Higgins in detail
Engineering Materials and Processes

24. 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
Engineering Materials and Processes

25. Precipitation from a solid solution (Higgins 9.4)
Follow notes in Higgins 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.
Engineering Materials and Processes

26. Ternary equilibrium. (Higgins 9.5)
Three metals, a 3D diagram!
Higgins RA & Bolton, Materials for Engineers and Technicians, 5th edition, Butterworth Heinemann. Ch 4
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27. Online Properties Resources.
Teach yourself phase diagrams
Handout
Wikipedia: Materials properties
Metal Grains and processing
h ttp://
S how this website on screen. Will be using this later.
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28. Coring or cored structure Dendritic Binary Tertiary Solid phase change
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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29. Define all the glossary terms.
QUESTIONS
Callister: Ch3 (Mostly about calculating atomic packing factors - too esoteric)
Moodle XML: Some questions in Classification and Steel
Define all the glossary terms.
There are two names for the same thing: Phase Diagram and Equilibrium Diagram. Both make sense. Describe what phase and equilibrium refer to.
Why would it be difficult to make an alloy of Rhenium and Cadmium?
Why is it important for a eutectic mixture to cool slowly during the creation of an equilibrium diagram?
What happens between the liquidus and solidus lines of a simple binary equilibrium diagram with complete solubility?
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?
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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