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Phase diagrams and the lever rule

When a Cu-Ni alloy is cooled under equilibrium through the temperature range where liquid and solid coexist, how do the compositions of the liquid and solid change?

  1. ABoth shift toward the Ni-rich side
  2. BBoth shift toward the Ni-poor (Cu) side
  3. CThe solid shifts toward the Ni-rich side and the liquid toward the Cu side
Show answer and explanation

Answer: B. Both shift toward the Ni-poor (Cu) side

In a two-phase region, the composition of each phase is given by the ends of the tie line at that temperature: the liquid on the liquidus and the solid on the solidus. In the Cu-Ni system, the liquidus and solidus are higher toward the side of Ni, which has the higher melting point (about 1455 °C), so as the temperature falls both ends of the tie line move toward Cu, which has the lower melting point (about 1085 °C). Both the solid and the liquid therefore lose Ni on cooling, while the amount of solid grows. The idea that the solid shifts toward Ni is a misconception arising from the fact that the first solid to form is Ni-rich. The overall alloy composition does not change, which is consistent with the lever rule showing the solid fraction increasing.

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More Phase diagrams and the lever rule questions

  1. When a Cu-Ni alloy is solidified with rapid cooling, as in actual casting, which correctly describes the composition at the center of a dendrite?
  2. The Al-Si system has a eutectic point at 577 °C and 12.6 wt% Si; at that temperature the Si solubility of the α (Al) phase is 1.65 wt%, and the Si phase can be taken as essentially pure Si (100 wt%). When an 18 wt% Si hypereutectic alloy is cooled under equilibrium to just above the eutectic temperature, which value is closest to the mass fraction of primary Si?
  3. At constant pressure, how many degrees of freedom are there at the eutectic point of a binary system (where a liquid and two solid phases coexist)?
  4. 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?
  5. 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?