Phase diagrams and the lever rule
Check Gibbs' phase rule, isomorphous, eutectic and peritectic phase diagrams, phase and microconstituent fractions by the lever rule, and the essentials of the Fe-C diagram with multiple-choice questions, and practice fraction calculations with explanations.
Phase diagrams and the lever rule: key points
A phase diagram shows which phases exist at equilibrium as a function of temperature and composition. For a binary system at constant pressure the phase rule becomes F = C − P + 1, so eutectic and eutectoid points, where three phases coexist, are invariant points with zero degrees of freedom. Learn to read the basic types: isomorphous systems such as Cu-Ni, eutectic systems such as Pb-Sn, and peritectic systems in which liquid and solid react.
In a two-phase region, the ends of the tie line give the composition of each phase and the lever rule gives the fraction of each phase. In the Fe-Fe₃C system, the eutectoid reaction at 0.76 wt% C and 727 °C produces pearlite; proeutectoid ferrite appears in hypoeutectoid steels and proeutectoid cementite in hypereutectoid steels. The key is to distinguish phases from microconstituents when calculating fractions.
All Phase diagrams and the lever rule questions (12)
- 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)?
- 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?
- 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?
- 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?
- Which equation represents a peritectic reaction? Write it in the direction of cooling.
- Which statement about the eutectoid point of the Fe-Fe₃C phase diagram is correct?
- 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.
- When a 1.2 wt% C hypereutectoid steel is slowly cooled from the austenite region, what microstructure is obtained at room temperature?
- 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%)?
- 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?
- 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?
- 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?