The Lever Rule

1
The Lever Rule

• The amounts of two coexisting phases are
  INVERSELY proportional to their distances from a
  point

2
Translating This Statement

• two coexisting phases
• Means you are in a 2 phase region.

• their distances from a point
• For a point C,

L
The distances are AC and CB
A L
B L
C
A B
A
B
3
Translating This Statement

• The amounts . . . Are inversely proportional
• Means AC / AB is the amount of B

L
B
And, CB / AB is the amount of A
A L
B L
A
C
A B
A
B
4
A Sample Calculation

• Draw a horizontal tie line through the point.

• Measure its length

• Measure the length of
• each side

L
C
D
AD 1 in.
AC .75 in.
CD .25 in.
A L
B L

• Calculate the amounts A L

A B
A
B
5
A more complex system . . .

• Draw a tie line.

• Identify the phases.

• Measure the line lengths.

• Calculate the amounts of
• each phase present.

A Li2O-B2O3
CB .562 in.
B Li2O-2B2O3
AC .188 in.
C
AB .75 in.
A
B
6
One Last Note.

• If a point is in a single phase region
  (including a solid solution), NO tie line is
  used. There is 100 of that phase.

C