ESO205 Nature and Properties of Materials

1)  (i) Draw a 'valid' binary phase diagram showing a eutectic reaction with the following characteristics. (i) Melting point (MP) of A > MP of B, (ii) the solubility of B in A is less as compared to A in B, (iii) maximum solubilities are obtained at the eutectic temperature. Let the components be 'A' and 'B'. Label the phase fields (using standard labels), axes, etc.

(ii) In a binary alloy show that the lever rule is a natural consequence of mass balance (i.e. for correct mass balance, the relative mounts of two co-existing phases or microconstituents must be as given by the lever rule).

2)  The Pb-Sn system shows the following eutectic reaction: .

In the microstructure of a Pb-Sn solder alloy, it was found that 88% of the area is occupied by the eutectic constituent and the remaining area by the proeutectic β phase. Assuming that the area fractions are equal to the volume fractions, determine the approximate composition of the alloy. The densities of α and β phases are 10,300 kg/m and 7300 kg/m.

3)  This problem pertains to the Ti rich portion of the Ti-Co phase diagram (for compositions upto Ti2Co). Liquid of 27wt. % Co, β of 17 wt. % Co and Ti2Co of 38 wt. % Co are in equilibrium at 1020°C. At 685°C, β of 8 wt. % Co, α of 1 wt. % Co and Ti2Co are in equilibrium. Data: , . β is BCC & α is HCP. Ti2Co is stable up to 1058°C.

(i) Draw the relevant portion of the phase diagram with requisite labels.

(ii) Describe the invariant reactions (with complete details). Use a graph paper to arrive at the diagram.

4)  (i) Draw the Fe-Fe3C phase diagram (till the liquid region).

(ii) Make neat sketches of microstructures expected for four compositions between 0.0 and 1.2% C: (i) C < 0.02 wt.% (passing through the a phase field and avoiding the eutectoid reaction), (ii) C slightly less than 0.8 wt.% (hypo-eutectoid composition), (iii) C = 0.8 wt.% (eutectoid composition), (iv) C slightly more than 0.8 wt.% (hyper-eutectoid composition). Assume slow cooling from the g phase field to room temperature.

5)  From the Fe-Fe3C phase diagram, for a 0.2% C steel, name the phases and their fractions at equilibrium at the following temperatures. (i) Just above 1493°C, (ii) Just below 1493°C, (iii) Just above 725°C, (iv) Just below 725°C.