Assignment: Phase Diagrams

1. Alloys of copper and zinc are called brasses. Two important commercial brasses are: 70/30 α-brass (containing 70 wt% Cu and 30 wt% Zn), and 60/40 α-β brass (containing 60 wt% Cu and 40 wt% Zn).

The phase diagram of Cu-Zn system is given below. Answer the following on the basis of the study of your diagram.

(a) What are the melting points of Cu and Zn? (b) Label all the two-phase fields on the phase diagram. (c) What is the approximate melting point of a 60/40 brass? (d) For 60/40 brass, determine the phases present, their compositions and their proportions at

950ºC, 850ºC and 700ºC. (e) Upon cooling of 60/40 brass from β phase field, at what temperature does α phase first

begins to appear? (f) Identify the invariant reactions taking place at 700º and 558ºC and write them completely.

2. Following details pertain to the Pb-Mg system:

(i) At 470°C compound PbMg2, liquid (80 atom% Mg) and β (92 atom% Mg) are in

equilibrium. (ii) At 250°C α (10 atom% Mg), liquid (20 atom% Mg) and PbMg2 are in equilibrium.

(iii) At RT, maximum solubility of Mg in α is 2 atom% Mg and that of Pb in β is 1 atom% Pb.

(iv) Melting points of Pb, Mg and PbMg2 are 327, 650 and 550 °C respectively.

Now attempt the following:

(a) Draw a schematic phase diagram of the system. (b) Immediately after the completion of the invariant reaction in an alloy containing 40 at%

Mg (i) What atom% of the alloy is proeutectic PbMg2?

(ii) What atom % of the alloy is PbMg2 which is contained in the eutectic solid?

(c) What is the fraction of Mg2Pb in an alloy of eutectic composition?

3. The eutectic reaction in Cr-Ni system is given as

L (49 wt% Ni) ⎯⎯⎯⎯→ α (35 wt% Ni) + β (53 wt% Ni) at 1345oC(a) Give the range of overall alloy composition for which eutectic mixture will not be present

in the microstructure of an alloy cooled slowly from the liquid phase to room temperature. (b) Suppose a Cr-Ni alloy of unspecified composition is held at 1350°C in the two-phase

(L+α) region. How many variables can you specify independently? Give reasons. (c) Consider two alloys of compositions Co and C1 where Co < CE and C1 > CE where CE is

the eutectic composition. The weight fraction of the proeutectic phase is the same for both, but immediately after completion of the eutectic reaction, the weight fraction of the total α for alloy of composition Co is 2.5 times the weight fraction of total α for the alloy of

composition C1. Determine Co andC1.

3. Fe-C phase diagram:(i) Samples of hypoeutectoid, eutectoid and hypereutectoid steel are cooled from 1000oC to room temperature. Sketch and label the expected microstructures of each sample at room temperature.(ii) Identify the various reactions in the Fe-Fe3C phase diagram.(iii) The microstructure of a steel consists of hypoeutectoid ferrite and pearlite; the weight fraction of these two constituents are 0.174 and 0.826 respectively. Determine the concentration of carbon in this alloy. Determine total weight fraction of ferrite in the alloy at room temperature.

4. Melting point of an element is 1050oC while that of element B is 1900oC. The solid solution containing 50% B, the solid solution 80% B and the liquid containing 30% B are in equilibrium at 1250oC. At the room temperature the maximum solubility of B in the phase is 30% and that of B in the phase is 10%.(i) sketch the phase diagram of the binary AB. Clearly indicate phases present in each region.(ii) what reaction takes place at 1250oC.(iii) what are the wt. fractions of phases present in the A-(75%)B alloy at 1251oC, 1249oC and room temperature.

5. In phase diagram on Ti-Ni system, identify the invariant points, writing down the reactions.

6. In aluminum-neodymium phase diagram, add the label to two phase region. Then specify temperature composition points at which all the invariant reactions occur, writing the proper reactions.

7. Phase diagram for the Cu-Ag system is given. For 25 wt % Ag, do phase analysis at 1000, 781, 779 oC in wt % and at %. If density of phase is 8.9 gm/cc and that of 10.5 gm/cc, also determine the volume fraction of each phase and microstructure constituents.

In addition to these questions, you should be well versed understanding relationship with G vs composition curves and thermodynamics.