1. Chemical compositions of equilibrated phases One phase areas: the determination of the chemical composition of a single phase is automatic: it has the same composition as the alloy. Two Phase areas: it is located at the two ends of the isotherm, or tie-line across the two-phase area.

3. Three-phase temperature and eutectic reactions Consider the Pb-Sn system separates into two solid phases (  and  ) at the eutectic temperature 183 o C. At this temperature only three phases can be in equilibrium. If this alloy is heated, the two solid phases of this solder melt into one phase liquid; Since the three phases of an eutectic reaction can coexist at only a specific temperature, this condition is called invarient. There is no choice of temperature other than 183 o C. There is no choice of phases – they must be  and  and the liquid.

4. Phase Rule P + F = C + 1 P = number of Phases C = number of components F = the variances or the degrees of freedom

6. 66% Ag 34% Cu 8% Ag 92% Cu

10. Chemical compositions of equilibrated phases One phase areas: chemical composition can be automatic; it has the same composition as the alloy

11. Two Phase areas The chemical composition of the 2-phase areas are located at the 2 ends of the isotherm, or tie-line

12. Quntities of phases in Equilibrated Mixtures One-phase areas: also automatic as previously indicated. When 200 g of liquid is present; the weight is 200 g. Two-phase areas: first determine the composition of the phases as we did by interpolation (tie-line) procedure.

14. For a given temperature and composition we can use phase diagram to determine: 1) The phases that are present 2) Compositions of the phases 3) The relative fractions of the phases Interpretation of Phase Diagrams

15. 1. Locate composition and temperature in diagram 2. In two phase region draw the tie line or isotherm 3. Note intersection with phase boundaries. Read compositions at the intersections. The liquid and solid phases have these compositions. Finding the composition in a two phase region

16. Finding the amounts of phases in a two phase region: 1. Locate composition and temperature in diagram 2. In two phase region draw the tie line or isotherm 3. Fraction of a phase is determined by taking the length of the tie line to the phase boundary for the other phase, and dividing by the total length of tie-line The Lever Rule

17. The lever rule is a mechanical analogy to the mass balance calculation. The tie line in the two-phase region is analogous to a lever balanced on a fulcrum.

20. The eutectoid (eutectic-like in Greek) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. Invariant point (the eutectoid) – three solid phases are in equilibrium. Upon cooling, a solid phase transforms into two other solid phases (d « g + e in the example below) Looks as V on top of a horizontal tie line (eutectoid isotherm) in the phase diagram.