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Phase diagrams and the lever rule

What is the main reason the maximum solubility of carbon is much larger in γ-iron (about 2.14 wt%) than in α-iron (about 0.022 wt%)?

  1. Aγ-iron has a lower packing factor than α-iron, so its total interstitial volume is larger
  2. BIn γ-iron, carbon dissolves not interstitially but by substituting for iron atoms
  3. CThe octahedral interstitial site of FCC γ-iron is larger than any interstitial site in BCC α-iron
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Answer: C. The octahedral interstitial site of FCC γ-iron is larger than any interstitial site in BCC α-iron

Carbon is an interstitial element that sits in the interstitial sites of iron. A sphere fitting the octahedral site of FCC γ-iron has a radius about 0.41 times that of the iron atom, whereas in BCC α-iron even the largest site, the tetrahedral site, is only about 0.29 times, and the octahedral site about 0.15 times. γ-iron can therefore accommodate carbon with less distortion. FCC actually has the higher packing factor (about 0.74, against about 0.68 for BCC), so the total interstitial volume is larger in BCC, and citing the packing factor gets it backward. What matters is that in BCC the free space is divided into many small holes. Carbon dissolves interstitially, not substitutionally.

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More Phase diagrams and the lever rule questions

  1. 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?
  2. 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?
  3. 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?
  4. 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)?
  5. 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?