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Phase diagrams and the lever rule

Which binary system is the classic example of an isomorphous phase diagram, with complete solubility in both the liquid and the solid over all compositions?

  1. AThe Pb-Sn system
  2. BThe Cu-Ni system
  3. CThe Fe-C system
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Answer: B. The Cu-Ni system

Cu and Ni are both FCC, differ in atomic radius by only about 2%, and have similar electronegativities and valences, so they satisfy the Hume-Rothery rules and form a substitutional solid solution at all compositions. The phase diagram is isomorphous, with a lens-shaped two-phase region bounded by two curves, the liquidus and the solidus. The Pb-Sn system has limited solid solubility and is the classic eutectic system, with a eutectic point at 183 °C. In the Fe-C system, carbon dissolves interstitially with low solubility, giving a complex diagram that includes eutectic, eutectoid and peritectic reactions.

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More Phase diagrams and the lever rule questions

  1. A Cu-35 wt% Ni alloy is held at a temperature where two phases coexist: liquid (31.5 wt% Ni) and solid α (42.5 wt% Ni). Which value is closest to the mass fraction of liquid?
  2. In the Pb-Sn system, take the eutectic temperature as 183 °C, the eutectic composition as 61.9 wt% Sn, and the compositions of the α and β phases at that temperature as 18.3 wt% Sn and 97.8 wt% Sn. When a 30 wt% Sn alloy is cooled under equilibrium to just below the eutectic temperature, which value is closest to the mass fraction of the microstructure that is eutectic structure?
  3. Which equation represents a peritectic reaction? Write it in the direction of cooling.
  4. Which statement about the eutectoid point of the Fe-Fe₃C phase diagram is correct?
  5. A 0.40 wt% C hypoeutectoid steel is cooled under equilibrium to just below 727 °C. Which value is closest to the mass fraction of proeutectoid ferrite? Take the eutectoid composition as 0.76 wt% C, the carbon content of ferrite at 727 °C as 0.022 wt% C, and cementite as 6.70 wt% C.