Question 1:

Define steady state diffusion and non steady diffusion, respectively, using words, equation or diagrams.

For steady state diffusion, Fick's first law applies, i.e.

J = -D dc/dx

Explain the variables and terms in this equation. Why is there a minus sign? What affects D?

For non-steady state diffusion, Fick's second law should be used. One for the analytical solutions corresponding to the following conditions

- At t = 0, C = C0 at 0 ≤ x ≤ ∞

- for t > 0, C = Cs at x = 0 and C = Co at x= ∞

Is Cx - Co/Cs - Co = 1 - erf (x/2√Dt)

Plot the composition profiles at t = 0 and t = t1 > 0, and annotate the graph.

Question 2:

Phase diagrams are usually equilibrium ones. What does equilibrium mean? How can equilibrium be achieved in cooling an alloy from liquid to solid at room temperature?

Draw schematically phase diagrams for an isomorphous system (i.e. the two components from complete solid solutions) and for a eutectic system, respectively. What can be read and calculated from the phase diagrams, given the composition and temperature?

In the eutectic system above, write down the eutectic reaction and draw the microstructure of the alloy with the eutectic composition after cooling down slowly from liquid.

In the eutectic system above, for an alloy with a composition which would result in a microstructure consisting of the primary α phase (α is the terminal solid solution on the left), secondary β phase (β is the terminal solid solution on the right), and eutectic structure following an equilibrium cooling from liquid to solid at room temperature, show how to calculate the amount of the eutectic structure and the amount of the secondary β phase.

Question 3: Can you sketch the microstructure of an Fe-3 wt% C alloy following cooling from the liquid state?

Question 4:

Think of all possible combination of phases (microstructures) that can be obtained using the transformation diagram.

Do we know whether a transformation will be accelerated or slowed down with increasing temperature?

How to promote the formation of martensite in order to achieve the tempered martensite microstructure?

Rank various microstructures in terms of strength and ductility, respectively.

Question 5:

Describe the similarities and differences between the treatments to obtain tempered martensite in steels and precipitation hardening in Al-Cu.

Why quenching is needed in age hardening?

How to choose and ageing temperature? Give an explanation based on the theories for strengthening and phase transformation.

Using heat treatment of steels as examples, appreciate the relationships between processing, microstructure and properties (e.g. spheroidite vs tempered martensite).