Phase Diagrams

1
Phase Diagrams

• Show the ranges of temperatures (and/or P) and
  composition over which phases or mixtures of
  phases of a compound or compounds are stable.
• Can also show existence of allotropes or
  polymorphism (solids having same composition, but
  different structure).
• Each phase occupies an area of the diagram.

2
Phase Diagrams

• Phase Rule P F C 2
• P of phases present in equilibrium.
• C of components needed to describe system.
• F degrees of freedom of independent
  variables that can be varied without changing the
  or composition of the existing phases.
• e.g. to right is 1 component (H2O) phase diagram.
  P F 1 2 3
• A at that point one phase (gas), so 2 degrees
  of freedom can change T or P.
• B at interface of liquid and vapor there are
  two phases, so 1 degree of freedom if change T,
  must also change P.
• C triple point, so no degrees of freedom
  changing either T or P changes composition.
• D critical point d(vapor) d (liquid).

D
B
A
C
3
Phase Diagrams

• First-order phase transition.
• Move from liquid to vapor temperature will stop
  changing at this point until all of the liquid
  becomes vapor and only then will continue to
  increase.

4
Binary Phase Diagram

• Phase diagram for two similar components aka
  Solid Solution.
• Assume Pressure 1 atm, so 2D rather than 3D
  plot.
• Two components, so F P 2 2 4
• Composition mole fraction 100 B to 100 A.
• Tm(B) melting point of pure B.
• Tm(A) melting point of pure A.
• Liquidous boundary between liquid and mixed
  phase gives liquid composition.
• Solidous boundary between solid and mixed
  phase gives solid composition.

Tm(B)
Tm(A)
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Binary Phase Diagram

• Heat mixture of A B (at mole fraction
  indicated) to temperature 1. Then cool.
• At temperature 1, liquid phase has composition
  mole fraction.
• At temperature 2, solid begins to ppt out solid
  is mostly B mixed crystal (composition b1).
• At temperature 3, solid has composition b2 and
  liquid has composition a2 note different mole
  fractions!
• at a given temperature, the liquid and solid that
  are in equilibrium with each other have different
  compositions.
• At temperature 4, solid formed has composition
  b3 original mole fractions.

1
2
3
4
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Binary Phase Diagram

• Note that on cooling, the solid will change
  composition from almost pure B to more and more A
  composition.
• Coring freeze in tube from outside core will
  have different composition.
• Heat Beat heat above liquidous, cool below
  solidous (but not too far), then beat (to make
  deformities), then reheat almost to solidous
  (increase diffusion), beat and repeat. Like?
  Blacksmith.

liquidous
solidous
B mole fraction A
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Binary Phase Diagram

• Example of a system involving the formation of
  mixed crystals with temperature minimum special
  point for which the compositions of the solid and
  liquid are the same.
• It is possible to have the special point at a
  temperature maximum.

liquid (1-phase)
liquid composition
solid composition
special point
solid (1-phase)
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Eutectic Phase Diagram

• What if two substances are NOT similar at all?
  They wont want to mix in the solid state, but
  will in the liquid e.g. NaF PbF2.

Eutectic Point (cusp) -eutectic mixture has lower
mp than either of the pure components or any
other mixture.
Tm(NaF)
liquid
Tm(PbF2)
liquidous curve -highest temp. at which crystals
can exist.
NaF(s) liquid
PbF2(s) liquid
NaF(s) PbF2(s) dont mix
solidous curve Eutectic Temperature -lowest
temp. at which liquids can exist.
NaF mole fraction
PbF2
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Eutectic Phase Diagram

• Heat above liquidous and cool first solid is
  pure NaF below Eutectic Temperature both solids
  appear.

Tm(NaF)
liquid
solid is pure NaF
Tm(PbF2)
liquid has increasing PbF2 fraction
NaF(s) liquid
PbF2(s) liquid
NaF(s) PbF2(s) dont mix
solid PbF2 begins to ppt
particles of NaF PbF2


NaF mole fraction
PbF2
pure NaF
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Phase Diagrams

• Have seen two extremes solid solution, where the
  two compounds like each other eutectic
  mixture, where the two compounds hate each
  other.
• What happens as the two compounds get away from
  these extremes?

Solid Solution
Eutectic Mixture
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Phase Diagram For Two Almost Immiscible Solids
region of solubility of A in B
region of solubility of A in B
always some width
e.g. most soldier is 5050 Pb/Sn heat to
solid/liquid region get solid particles in
slushy soldier liquid
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Phase Diagram If Two Components Form 3rd Compound

• Looks like two Eutectic Diagrams next to each
  other.

new compound melts congruently
Two Eutectic Points
Compound Forms called line compound