The Lever Rule

1
The Lever Rule

• Ceramic Engineering 251
• Courtney Peace
• Fall Semester 2000

2
Binary Phase Diagrams

• Condensed system assumes a constant pressure.
• Between the end members, there are intermediate
  mixtures of components A and B.

3
A Question

• How do we determine the amount and composition of
  the phases present at any temperature if we know
  the relative amounts of the two end members ?

The Lever Rule
4
To Apply the Lever Rule

• Locate the composition (60 B, 40 A).
• Draw a vertical line at that composition.

5
The Next Step

• Then identify the critical temperatures for
  analysis 850 and 550.

6
Analyzing the First Temperature

• Above 850C, the only phase present is liquid.
• Just below 850C, draw horizontal line from the
  intersection of the vertical line and the curve
  to the B end member.

7
Print to continue analysis
8
Analyzing the First Temperature

• This line is 60 mm long.
• The composition is 100 liquid, of the 60 B,
  40 A composition.
• Total A 40
• Total B 60

60 mm
9
Analyzing the Second Temperature

• Above 550C, the line is divided into 34 mm and
  60 mm sections.
• The left section (34 mm) is the proportion of
  solid (B). The right section (60 mm) is the
  proportion of liquid, of the circled composition.

34 mm
60 mm
10
Determining the Liquid Composition
Determining the Liquid Composition

• The composition of the liquid at 550C is 38 B
  and 62 A.
• Total A
• 60/(3460)38 40
• Total B
• 60/(3460)62
• 34/(3460)100 60

34 mm
60 mm
11
Analyzing the Final Temperature

• Below 550C, only solids A and B are present.
• The line is divided into 2 sections 90 mm (B)
  and 60 mm (A).

60 mm
90 mm
12
The Final Step

• The line is divided into 90 mm (B) and 60 mm (A)
  sections.
• Total A
• 60/(9060) 40
• Total B
• 90/(9060) 60

60 mm
90 mm
13
Conclusions

• If the relative amounts of the two end members
  are known, it is possible to find the composition
  of each phase at any temperature.
• At any temperature, the overall amounts of A and
  B should be the same.