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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2026 · Paper I

Q3(a)(ii). Cd–Bi simple eutectic: phase diagram and cooling curves

  • 10 marks
  • Answered
Question

Cadmium (m. pt. = 321°C) and bismuth (m. pt. = 271°C) do not form solid solutions or compounds with one another. Their eutectic point lies at 61 weight percent of bismuth and 146°C. Sketch their phase diagram and label each region to show what phases are present. Explain the cooling curves of this eutectic mixture.

Answer in brief

A simple eutectic diagram: two liquidus curves fall from 321°C (Cd) and 271°C (Bi) and meet at E (61 % Bi, 146°C). The 61 % melt cools to 146°C and then shows a single long halt, like a pure metal; any other alloy shows a break at the liquidus and then the same halt at 146°C.

Key points

  • Pure Cd (or pure Bi). The melt cools smoothly. At 321°C solid appears: C=1, P=2, F'=1-2+1=0, so the temperature stays constant (a halt) until all the metal has solidified. Then the solid cools.
  • An alloy with 40 % Bi (isopleth a). The melt cools steadily until it meets the liquidus. Pure Cd starts to crystallise. Its latent heat slows the cooling, so the curve shows a break (change of slope), not a halt: P=2, F'=1,…
  • The liquid reaches E at 146°C. Bi(s) now separates as well, P=3 and F'=0: a eutectic halt until the remaining liquid has frozen. Just above 146°C the lever rule gives primary Cd =(61-40)/61=34 % and liquid =66 % of the mass;…
  • The eutectic mixture itself (61 % Bi, isopleth e). No solid separates above 146°C, so there is no break. At 146°C Cd and Bi crystallise together, the liquid keeps its composition, and F'=0 gives one long halt. The whole sample…

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

The regions

RegionPhases presentPF'
Above both liquidus curvesone liquid melt (L) of Cd and Bi12
Left, above 146°CL + solid Cd21
Right, above 146°CL + solid Bi21
On the line at 146°CL (composition E) + Cd(s) + Bi(s)30
Below 146°CCd(s) + Bi(s): primary crystals in a fine eutectic mixture21

Each liquidus is a freezing-point curve: Bi lowers the melting point of Cd, and Cd lowers that of Bi. With no solid solutions, the solid that separates is the pure metal.

The cooling curves

  1. Pure Cd (or pure Bi). The melt cools smoothly. At 321°C solid appears: C=1, P=2, F'=1-2+1=0, so the temperature stays constant (a halt) until all the metal has solidified. Then the solid cools.
  2. An alloy with 40 % Bi (isopleth a). The melt cools steadily until it meets the liquidus. Pure Cd starts to crystallise. Its latent heat slows the cooling, so the curve shows a break (change of slope), not a halt: P=2, F'=1, and the temperature still falls as the liquid becomes richer in Bi along the liquidus.
  3. The liquid reaches E at 146°C. Bi(s) now separates as well, P=3 and F'=0: a eutectic halt until the remaining liquid has frozen. Just above 146°C the lever rule gives primary Cd =(61-40)/61=34 % and liquid =66 % of the mass; this 66 % freezes in the halt.
  4. The eutectic mixture itself (61 % Bi, isopleth e). No solid separates above 146°C, so there is no break. At 146°C Cd and Bi crystallise together, the liquid keeps its composition, and F'=0 gives one long halt. The whole sample freezes here, so this is the longest halt of all the compositions.
  5. The eutectic melts sharply like a pure substance, but it is not a compound: under the microscope it is two solid phases, and its composition shifts if the pressure is changed.
  6. Alloys with more than 61 % Bi behave as in 2 and 3, with Bi separating first. The length of the eutectic halt rises from zero at 0 % to a maximum at 61 % and falls to zero at 100 % Bi; plotting it locates E.

Application. thermal analysis: the breaks and halts of a set of cooling curves give the points of the phase diagram. Low-melting eutectics are used as solders and fusible alloys; the tin–lead eutectic solder (about 62 % Sn, 63/37' solder) melts sharply at 183°C.

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Model answer to Q3(a)(ii), 2026 Paper I: solution page 16
Solution page 16 of 55
Read the whole 2026 solution2026 question paper

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