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Phase Diagrams

What are they?

You should know that a chemically pure substance (an element or compound) has a sharp, clearly defined melting point. Mixtures tend to solidify over a temperature range, that is they start to solidify at one temperature and do not complete the process until they reach a lower point. What you may not know is that the temperature range depends on the precise mixture; a mix of 80% A with 20% B will solidify over a different range than a mix of 20% A with 80% B. A phase diagram allows us to present all this information in a single (sometime simple) diagram.

 Cooling Curve: Pure 

Phase diagram of Copper Nickel Alloy

When the mixture is made mostly of metals at is called an alloy and so phase diagrams are vitally important for engineers and metallurgists since it gives information about how the solid alloy forms, what its chemical composition is and what its microscopic structure will be.

How to read them

The vertical scale give the temperature and the horizontal axis gives the composition.

If you draw a vertical line at the 60% Ni line one can find out about an alloy made of 60% nickel and 40% copper. As you move down the line from a high temperature you eventually meet the liquidus line this is the point at which the molten alloy (the melt) starts to solidify.

You might be tempted to assume that the temperature reduces until the vertical line touches the solidus line and that the whole solid is uniformly made up of the original composition. Things tend to be a little more complicated though.

Cooling Curve: Pure 

Solidification of 60% Ni 40% Cu Alloy

Assuming that the cooling happens slowly the following happens:

'Simple' phase diagrams like this occur when the metal atoms are of:

This allows atoms of either variety to replace each other without disturbing the growing crystals. In effect the two atoms varieties can form a solid solution, regardless of the composition. The word to describe this is ‘isomorphous’.

Element

Symbol

Atomic Radius (nm)

Electronegativity

Valency

Crystal Structure

Aluminium

Al

125

1.61

3

Face Centred Cubic

Antimony

Sb

145

2.05

3, 5

Rhombohedral

Copper

Cu

135

1.90

1, 2

Face Centred Cubic

Gold

Au

135

2.54

1, 3

Face Centred Cubic

Lead

Pb

180

2.33

2, 4

Face Centred Cubic

Molybdenum

Mo

145

2.16

3, 5, 6

Body Centred Cubic

Nickel

Ni

135

1.91

2, 3

Face Centred Cubic

Niobium

Nb

145

1.60

3, 5

Body Centred Cubic

Silver

Ag

160

1.93

1

Face Centred Cubic

Tin

Sn

145

1.96

2, 4

Tetragonal

Tungsten

W

135

2.36

6

Body Centred Cubic

Unfortunately things are not always so simple. For most alloys systems there is a limit to how much of a given atom species can be absorbed and this produces far more complex diagrams. In the following diagram the αPb area on the left hand side is a solid solution of tin in lead, this cannot be greater than about 19% Sn. Similarly the βSn area on the right is a solid solution of lead in tin, this can be a maximum of only 2.5% Pb. Lead is a considerably larger atom that tin and so easily disrupts the regular arrangement of the tin atoms.

Cooling Curve: Pure 

Phase diagram of Lead Tin Alloy

If you draw a vertical line at the 5% Sn line you can find out about an alloy made of 5% tin and 95% lead. As you move down the line from a high temperature you eventually meet the liquidus line this is the point at which the molten alloy (the melt) starts to solidify.

If you think back to ‘simple' phase diagrams you should be able to work out what happens to the 5% tin alloy as it solidifies. The liquid cools until it reaches the liquidus line at about 320 °C. grains of αPb then start to form with a composition of about 2% tin, 98% lead.

When the temperature has reached 310 °C the grains make up about two thirds of the semi‑molten (mushy) mixture. The grains are being coated with αPb with a composition of about 3.7% tin, 96.3% lead and the liquid has a composition of about 6% tin, 94% lead.

At slightly above 300 °C the last of the liquid has a composition of about 11% tin, 89% lead and the final grains have a uniform composition of 5% tin due to diffusion in the grains. The whole solidification process has taken place over a temperature range of slightly less than 20 °C and the process was very similar to the simple copper – nickel alloy dealt with previously.

Cooling Curve: Pure 

What happens though if the concentration of tin is increased to 20%?

Cooling Curve: Pure 

Firstly the temperature drops until the liquidus line is reached at about 290 °C (point a). At his point grains of αPb start to form with a composition of around 8% tin, 92% lead. As the liquid has only 80% lead this enriches the liquid with tin.

By the time the temperature has fallen to 250 °C (point b) αPb grains are being laid down with a composition of about 13% tin, 87% lead and the melt has a composition of around 36% tin. 64% lead.

The temperature continues to drop through 200 °C (point c) where the αPb grains are being laid down with about 18% tin, 82% lead and the melt at around 56% tin. 44% lead, massively enriched in tin although by now the solid makes up about 90% of the total material.

At 183 °C (point d) the last of the liquid has a composition of 63 % tin, 37% lead (point E). You might expect the grains to be composed of 20% tin but this is not the case since the maximum tin content of αPb is 19%. Instead βSn starts to form in the liquid with a composition of 97.5% tin, 2.5% lead, the maximum it can possibly be. As soon as this happens the remaining liquid becomes enriched in lead (because so much tin is being drawn out) and so a thin layer of αPb forms on the top. This makes the liquid tin rich again and so βSn forms on top. This process flips back and forth until all the liquid has been used up and the whole solidification process took place over a temperature range of over 100 °C.

The result of the cooling process so far are grains of αPb (19% tin, 81% lead) with small patches of layered αPb - βSn. But even though the alloy is solid the process still hasn’t finished. As the material cools to room temperature the αPb can hold on to less and less tin, and the same process happens with the βSn. This is shown by the curved, dashed lines beneath the solidus line. The end result is that the solid is largely made up of quite pure αPb embedded with tiny islands of tin with patches of layered αPb - βSn with their own islands of tin and lead respectively.

In summary: alloys can be complex.

What happens though if the concentration of tin is increased to 63%? This is a very peculiar temperature since the liquid cools down to the point marked E at a temperature of 183 °C and stays there. At some points in the liquid grains of αPb start to grow and at others, grains of βSn are created. Wherever the αPb grows the liquid rapidly becomes richer in tin so βSn begins to grow over the top. The reverse process happens with the βSn that gains a coating of αPb. As soon as the coating forms the liquid becomes enriched the other way and so the process continually repeats until all the the liquid is used up. The entire process happens at the fixed temperature of 183 °C. Once the alloy is fully solid the temperature can begin to drop again.

Many alloys possess a point like this, it is called the eutectic point and such alloys are called eutectic alloys. In the case of the lead – tin system the layers (called lamella) rapidly break down, in other alloys they remain stable at room temperature, in steel the lamellae areas are called 'pearlite'.

Cooling Curve: Pure 

Solid Solutions?

All the alloys you have looked at this page have been to some extent 'solid solutions' of one element in another. ‘Substitutional’ alloys happen when an atom of one material can replace an atom of another material without too much disturbance to the crystalline structure of the alloy grains. An example of this type of alloy is the copper – nickel family of alloys. ‘Interstitial’ alloys happen when an atom of one material can fit into the gaps between the atoms of the main material. The most widespread example of this is steel, where the relatively small atoms of carbon fit (roughly) in to the gaps between iron atoms.

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