# 12.11: Questions

- Page ID
- 36307

## Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

What is the effect on the shape of the free-energy curve for a solution if its interaction parameter is positive?

**Answer**- C

In terms of interatomic bonding, what does a negative interaction parameter represent?

**Answer**- B

Cooling curve for a binary system:

**Answer**- C

What is a hypoeutectic alloy?

**Answer**- B

Look at the following Al-Si phase diagram. (Place the mouse over the diagram to determine the temperature and composition at any point.)

For an Al 5 wt% Si alloy what will be the composition of the solid in equilibrium with the liquid at 600�C?

**Answer**- A

Look at the following Cu-Al phase diagram. (Place the mouse over the diagram to determine the temperature and composition at any point.)

What will be the relative weight fraction of CuAl_{2} (θ) in a Al 15wt% Cu alloy at its eutectic temperature?

**Answer**- B

## Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

Using the following data, calculate the volume fraction of the beta phase and eutectic at the eutectic temperature, for an alloy of composition 75 wt% Ag. Assume equilibrium conditions.

At eutectic temp:

eutectic composition = 71.9 wt% Ag

maximum solid solubility of Cu in Ag = 8.8 wt% Cu

density Ag = 10 490 kg/m^{3}

density Cu = 8 920 kg/m^{3}

**Answer**-
Using the lever rule, fraction of beta

= (

*C*-*C*_{1}) / (*C*_{2}-*C*_{1}) = (75 - 71.9) / (91.2 - 71.9) = 16 wt%.So fraction of eutectic

= 84 wt%.

To convert to volume fractions, we need to calculate densities of beta and eutectic.

Density of eutectic

= 0.719 x 10 490 + 0.281 x 8 920 = 10 049 kg/m

^{3}.Density of beta

= 0.912 x 10 490 + 0.088 x 8 920 = 10 352 kg/m

^{3}.Therefore, volume fraction of beta

= (10 049/10 352) x 16 = 15.53 vol%.

Hence volume fraction of eutectic

= 84.47 vol%.

Composition vs temperature phase diagrams exist for the combinations of three elements A, B and C (i.e. the three phase diagrams A-B, A-C and B-C). How might they be arranged in three-dimensional space to construct a "ternary" phase diagram for a system containing A, B and C?

Hint: Consider the possible extreme compositions.

**Answer**-
The phase diagrams must be constructed into a triangular prism:

The rectangular faces of the prism represent binary states. The corners represent 100% pure states of A, B and C. Inside the prism details the phases of the system with varying compositions of the three elements. The phase boundary lines of each binary phase diagram extend into the prism.

## Open-ended questions

The following questions are not provided with answers, but intended to provide food for thought and points for further discussion with other students and teachers.

Under what conditions could the compositions of the phases present differ from that predicted in the phase diagram?