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The Lever Rule In Binary Systems

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The first step in lever rule calculation is to draw a tie line through the ... the lengths of the tie line, and the distance from the composition to each phase. ... – PowerPoint PPT presentation

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Title: The Lever Rule In Binary Systems


1
The Lever RuleIn Binary Systems
  • The relative 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
  • Pick an arbitrary point C,

L
The distances are AC and CB
A L
B L
C
A B
A
B
3
Tie Lines
  • The line from A to B through C is a tie line.
  • A tie line is,
  • An isothermal line
  • That connects two equilibrium phases

4
Translating This Statement
  • The amounts . . . Are inversely proportional
  • Means AC / AB is the fraction of B

L
B
And, CB / AB is the fraction of A
A L
B L
A
C
A B
A
B
5
A Sample Calculation
  • Draw a horizontal tie line through the point.
  • Identify the phases.
  • Measure its length

L
L (liquid)
  • Measure the length of
  • each side

C
D
AD 1 cm
A L
B L
AC .75 cm
CD .25 cm
  • Calculate the amounts A L

A B
A
B
A (solid)
6
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 cm
B Li2O-2B2O3
AC .188 cm
C
AB .75 cm
A
B
7
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
8
Summary
  • The lever rule is used to calculate the relative
    percents of each phase when 2 or more phases are
    present.
  • The first step in lever rule calculation is to
    draw a tie line through the composition.
  • Next one measures the lengths of the tie line,
    and the distance from the composition to each
    phase.
  • The relative concentration of a phase is
    proportional to the distance from the other phase
    to the composition, divided by the length of the
    tie line. (Opposite length / total length)
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