Phase Diagrams

Part 2

Inverse Lever Rule:

Inverse lever rule is used to determine the percentage of each phase that is present at various temperatures.

The length of line XY represents the sum of the two phases as 100 percent. The inverse lever rule states that liquid phase can be calculated by taking the length of the line XZ and dividing this by XY.

The solid phase can be calculated by taking the length of the line ZY and dividing it by XY. To get the percentages, the values are multiplied by 100.

Figure 1. Phase diagram of a mixture with complete solubility in liquid and solid states.

Sample Calculation :

Alloy with 40 % A and 60 %B at room temperature is heated to a temperature T1 . Calculate the liquid and solid phase and indicate the composition of each phase.

Liquid Phase =( XZ / XY) x 100 = [(40-10) / (70-10)] x100 = 50%

Solid Phase = ( ZY / XY) x 100 = [(70-40) / (70-10)] x100 = 50%

At temperature T1, the solid composition is found by the intersection (point X) of isothermal line T1 and the solidus curve.

Solid composition: 10 % A and 90 % B

The liquid composition at temperature T1 is found by the intersection (point Y) of isothermal line T1 and the liquidus curve.

Liquid composition: 70% A and 30 % B

 

Eutectic System:

Eutectic system is a phase transformation that takes place when a single-phase liquid transforms directly to a two-phase solid.

L ---> S1 + S2

Liquid ---> Solid 1 + Solid 2

(This is a reversible phase transformation)

Figure 2. Eutectic phase transformation.

Eutectoid System:

The eutectoid phase transformation occurs when a single-phase solid transforms directly to two-phase solid.

S1 --->S2 + S3

Solid 1 ---> Solid 2 + Solid 3

(This is a reversible phase transformation)

Figure 3. Eutectoid phase transformation.

 

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Last Updated : September 17, 1999

By: Serdar Z. Elgun