Phase Diagrams

Question 1

Define a phase

Answer 1

All parts of a material with the same atomic structure are a single phase

Question 2

Define Solid Solution

Answer 2

A solid solution is a solid in which one or more elements dissolved such that they are homogeneously dispersed.

Question 3

What is the constitution of an alloy

Answer 3

The constitution is described by:

1. Phases present
2. Weight/Atomic fraction of each phase
3. Composition of each phase

Question 4

Define the Gibbs Free Energy Function

Answer 4

G = U + pV - TS = H - TS

Question 5

Define the equilibrium constitution

Answer 5

The equilibrium constitution is the state of lowest Gibbs free energy for a given composition at given temperature and pressure.

Question 6

Define a Phase Diagram

Answer 6

A phase diagram (also known as an equilibrium diagram) is a diagram with the Temperature and Composition as axes. Remember that since we are slow cooling that the overall alloy composition never changes only the phases and their relative proportions (as governed by the lever rule)

Question 7

Define the Liquidus and Solidus Phase Boundaries

Answer 7

The phase boundary that limits the bottom of the single-phase liquid field is the liquidus boundary and the phase boundary that limits the upper bound of the single phase solid field is the solidus boundary.

Question 8

Describe the key features of the cooling curve for an alloy

Answer 8

For pure metals the cooling cover contains arrest points where the pure metal changes states. These arrest points correspond to the release of a latent heat. However, for an alloy solidification occurs over a range of temperatures (as it is a mixture) so there are no arrest points but the cooling rate slows as the alloy passes through phase boundaries as latent heat is being released.

Question 9

What is unique about the Cu-Ni Phase Diagram

Answer 9

Cu-Ni can form a single phase solid solution at any composition at low temperature so there are no solvus boundaries

Question 10

What phases are present either side of the solvus boundaries.

Answer 10

2 phases are present. Either side of true solvus boundaries will be single phase regions e.g Pb-rich and Sn-rich solids.

Question 11

What is the eutectic point

Answer 11

The lower limit of the single phase liquid region formed by the intersection of two falling liquidus lines is known as the eutectic point. The eutectic point also gives the lowest temperature at which the 100% liquid is stable.

Question 12

What is the phase constitution in single phase region

Answer 12

At a constitution point in a single phase region the phase composition is the composition of the alloy itself

Question 13

In a two phase region how do we determine the phase composition

Answer 13

In a two phase region the phase compositions lie either side of a horizontal line that passes through the constitution point.

Question 14

Define the Lever Rule

Answer 14

If the x-axis is in wt% we measure the the length of the tie line and the relative proportions of the phases is given by the length of each section divided by the total length of the tie line.

If the x-axis scale is in at% then we cannot use the lengths of the segments and instead we find the difference in at% and calculate the same ratios: a/l and b/l

Question 15

Explain the origin of Intermediate Compounds

Answer 15

Thermodynamically, compounds form because the the particular combination of components is able to form as a single phase with a lower free energy than a mixture of two phases. These compounds have higher melting points as they are thermodynamically more stable.

Question 16

Name some examples of uses of iron-carbon alloys

Answer 16

1. Cast iron brake discs
2. I-Beams
3. Car Bodies

Question 17

Name the three phases of Iron and at what temperature they are found

Answer 17

1. Ferrite (alpha) is BCC is the low temperature form
2. Austentite (gamma) is FCC is the medium temperature form
3. Delta is BCC is the high temperature form

Question 18

Outline the key features of the cooling curve for Iron

Answer 18

The cooling curve will feature arrests due to the release of latent heat as it undergoes phase transformations from delta to gamma and finally to alpha. The arrests on the cooling curve are much smaller than that seen for changes of state since the latent heat release is much smaller

Question 19

How does the solubility of carbon in Iron vary with the microstructure of the Iron

Answer 19

In FCC the interstitial holes are larger than BCC leading to higher solubility of Carbon. Therefore the size of the interstitial spaces determines the extent to which iron dissolves carbon to form a single phase.

Question 20

What is the composition of Cementite

Answer 20

Cementite is Iron Carbide (Fe3C). It can be seen a thin vertical strip on the right side of the Iron-Carbon phase diagram above 7 wt% C

Question 21

What is a eutectoid point

Answer 21

The lower limit of a single phase solid field formed by the two falling phase boundaries intersecting in a V shape is called the eutectoid point

Question 22

What is a Peritectic point

Answer 22

An inverted V meeting a horizontal line giving the maximum temperature at which the enclosed liquid phase(s) form.

Question 23

Why is Iron Carbide metastable

Answer 23

The Iron Carbon diagram is not strictly an equilibrium diagram. Iron Carbide (Cementite) is in a metastable state. Thermodynamically, a true stable state would be a two phase mixture of Iron and Carbon (like Pb-Sn). However, in most cases Iron Carbide forms in preference to Carbon showing that the mechanism of the phase transformation takes priority over free energy minimisation.

Question 24

Why do phase transformations take place

Answer 24

When temperature varies in a process the equilibrium condition of the material keeps changing. These phase transformations determine what phases are present and therefore the final microstructure and material properties.

Question 25

Outline the mechanism of solidification of pure metals

Answer 25

1. Homogenous Nucleation - the solid colonies spontaneously form and grow stable provided they reach a critical radius. Heterogeneous nucleation facilitates the process with solid nuclei forming more readily on the pre-existing solid.
2. Each region grows by atoms transferring at the solid-liquid interface
3. Growth continues until impingement occurs - which is a misfit in the atomic packing
4. The individual crystallise remain identifiable by their grain boundaries.

Question 26

Define Eutectic Solidification

Answer 26

A eutectic reaction is a three phase reaction by which on cooling a liquid transforms into two solid phases at a constant temperature

Question 27

What is the microstructure of eutectic solidification

Answer 27

The two metals inter diffuse to generate solid regions in which each dominates. This occurs over small diffusion distances resulting in an intimate mixture of the two phases.

Question 28

Why are the shape of the phases in a eutectic solid plate/needle-like

Answer 28

• Minimise diffusion distance resulting in an intimate mixture of the two phases
• Reduced surface energy allowing for faster growth

Question 29

Define off-eutectic solidification

Answer 29

Off-eutectic solidification occurs when the composition of the alloy being cooled is not equal to the eutectic composition.

Question 30

Describe the micro-structural changes that occur when slow cooling off-eutectic solids (use Pb-Sn as example)

Answer 30

1. Start as a single phase liquid
2. As the liquidus line is reached nuclei of Pb-rich solid appear
3. This nucleation of rich solid in the liquid phase ends at the eutectic temperature
4. At the eutectic temperature the remaining liquid undergoes eutectic solidification. (Lamellar Structure)
5. As the alloy is cooled to room temperature, the Sn-rich solid precipitates out.

Question 31

How can we visually distinguish off eutectic solidification

Answer 31

Off eutectic solidification results in large plate like structures. These structures are the remnants of the rich solid nucleating after passing through the liquid phase.

Question 32

Define the eutectoid reaction

Answer 32

A eutectoid reaction is a three phase reaction by which, on cooling, a single phase solid transforms into two different solid phases at constant temperature.