Interpretation of Phase Diagrams

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Chapter 6

• Interpretation of Phase Diagrams

Phase diagrams summarize in graphical form the
ranges of temperature (or pressure) and
composition over which phases or mixtures of
phases are stable under conditions of
thermodynamic equilibrium. Phase diagram
contains information of compounds composition,
solid solution, phase transition and melting
temperature.
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Phase rule P F C 2

• P number of phases
• C number of components
• F degree of freedom

PV nRT 3 variables, 1 equation
Total number of degree of freedom (C-1)P
2 Number of relations C(P-1) Net degree of
freedom F (C-1)P 2 C(P-1) C P 2
C1 C2 .. Cc 100
P-1 relations m1 m2 m3 m4 m5 . mP
mi free energy
One needs P-1 equations to describe the
equilibrium between phases
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P number of phases

• How to distinguish phases?
• l   crystalline phases MgSiO3, Mg2SiO4
• l   polymorphism a- b- g-
• l   solid solution ( one phase )
• l   defects
• ordered defects distinguished
  phases
• disordered defects one phase
• (considered as solid solution)
• WO3-x (WnO3n-1 W20O59, W19O56)
• l   liquid (miscibility or immiscibility)
• l   gas one phase
•  
•  

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C number of components

• CaO-SiO2 two components
• MgO (heating below mp) one component
• FeO appears to be one component, but two
  components

? 3Fe2 ? 2Fe3 Feo ? FeO is in fact Fe1-xO
(wüstite) x Fe
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Phase diagram of CaO-SiO2
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F degree of freedom

• Independent variable to describe a system

For example boiling water P 2, C 1 F C
P 2 1 - 2 2 1 So only temperature or
pressure is enough to describe the system, that
is, T and P are dependent variables.
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Thermodynamically stable or kinetically stable
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How do you know a compound is thermodynamically
stable or kinetically stable?

• eg. 1. Ca3SiO5 is prepared above 1300oC.
• At 1100oC, Ca3SiO5 ? CaO Ca2SiO4
• Ca3SiO5 is thermodynamically stable above
  1300oC but is kinetically stable at 1100oC.
• eg. 2. At ambient temperature and pressure,
  graphite is thermodynamically stable and diamond
  is kinetically stable.

Usually metastable products can be obtained by
quenching the reaction before it reaches
equilibrium.
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One component system

• F C P 2 3 P
• One phase, P 1, F 2
• It takes two independent variables to
  describe the system. Ex. Ideal gas law PV nRT
• Two phases, F 1,
• e.g. Boiling water. Need to know P or T.
• Three phases no variables.

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One component system
BE gives the change of transition temperature
with pressure. (F 1) FC change of melting
point of polymorph Y with pressure. (F 1) AB,
BC sublimation curves for X and Y. (F 1)
CD vapour pressure curve for the liquid. (F
1) Points B, C are triple points. (F 0) In area
X, Y etc, F 2
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Phase diagram of water
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Phase diagram of SiO2
At 1600 bar

• a-quartz ? b-quartz
• liquid SiO2
• ? b-tridymite and
• b-cristobalite have lower density than quartz

However, many metastable phases can be obtained
by quenching.
At 500 bar
a-quartz ? b-quartz? b-tridymite ? b-cristobalite
? liquid SiO2
573oC
870oC
1470oC
1710oC
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Condensed System

• For most systems and applications of interest
  in solid state chemistry, the condensed phase
  rule is applicable, pressure is not a variable
  and the vapour phase is not important.

Condensed Phase Rule P F C 1
e.g. SiO2 (Fig 6.5) 1 F 1 1 gt F
1 So that temperature is the only factor for
the change of polymorphs
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Eutectic Binary System
y invariant point xyz liquidus curve cyd
solidus curve
eutectic point
What happens if the system is heated from
points e and f ?
In order to determine the relative amounts of two
phases in a mixture, the level rule is used
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Level Rule
(amount of liquid) x (distance of hf) (amount
of B) x (distance of Bf)
(amount of B) hf/Bh (amount of liquid) Bf/Bh
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B
Liquid
(amount of B) hf/Bh (amount of liquid)
Bf/Bh Composition of liquid h
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Amount of liquid in varies T

• T1 0.43 (43 liq.)
• T2 liq in f Bf/Bj 0.53
• T3 0.71
• T4 melt complete

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Eutectic Reaction

• Reactions at f point
• T gt T1 57 B (43 liq.)
• T lt T1 70 B (30 A)
• mixture of A B crystallized
• The reaction described above are those that
  should occur under equilibrium conditions.

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A method to lower melting point

• From the eutectic binary system, it can be
  considered that B is added to lower the melting
  point of A.
• For example, NaCl is added to lower the
  melting point of ice (to 21 oC)

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Binary systems with the formation of compounds
Point x peritectic point. Compound AB melts
congruently or incongruently.
Describe what happens when system is cooled at
composition n ?
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Non-equilibrium products

• Describe what happens when system is cooled
  at composition n ?

When the system is cooled at composition n, one
should get AB B (equilibrium product) But if A
L ? AB L is very slow, one will get A AB
B ( non-equilibrium products)
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Phase diagram of CaO-SiO2 system
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Immiscible Liquids
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Formation of metastable 2-liquid system
It happens when 2-liquid ? B liquid is very
slow upon cooling
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Binary system with complete range of solid
solution
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Cored (phenomenon of non-equilibrium)

• When the system is cooled at composition b,
  the central part that forms first may have
  composition a and on moving out radially from the
  centre the crystal becomes increasingly rich in B.

Still forms a single crystal (the same structure
type of A and B) but with concentration gradient.
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What forms solid solution?

• A and B have the same structure type and ions
  in them have similar size.

e. g. CaAl2Si2O8 and NaAlSi3O8 in plagioclase
feldspar system
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The plagioclase feldspar system
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Glass formation

• Recently, there has been much scientific and
  technological interest in glassy semiconductors
  and metals, materials with unusual electrical and
  mechanical properties.

If the liquid is cool rapidly (quenched) to room
temperature, there may not be time for any
crystallization to occur and a glass forms.
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Partial Solid Solution

• If ions are quite different in size
• ? complete solid solution may not be possible.
• e.g. forsterite (Mg2SiO4) vs willemite (Zn2SiO4)

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Partial Solid Solution
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A slightly complicated partial solid solution
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A complicated Partial Solid Solution
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Binary system with polymorph transitions
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example
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Another example
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The Fe-C diagram