Transcript PowerPoint 簡報 - National Chung Cheng University

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
compound’s composition, solid solution, phase
transition and melting temperature.
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)
C1 + C2 + …..+ Cc = 100%
Net degree of freedom: F = (C-1)P + 2 – C(P-1) = C – P + 2
P-1 relations: m1 = m2 = m3 = m4 = m5 = …….= mP mi: free energy
One needs P-1 equations to describe the equilibrium between phases
P: number of phases
How to distinguish phases?
l
l
l
l
crystalline phases: MgSiO3, Mg2SiO4
polymorphism a- b- gsolid solution ( one phase )
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
C: number of components
a)
b)
c)
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
Phase diagram of CaO-SiO2
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.
Thermodynamically stable
or kinetically stable
uns table
m e tas table
(kinetically stable)
s table
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.
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.
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
Phase diagram of water
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
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 => F = 1
So that temperature is the only factor for the change
of polymorphs
Eutectic Binary System
eutectic point
y: invariant point
xyz: liquidus curve
cyd: solidus curve
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
Level Rule
liquid
f
h
B
B
(amount of liquid) x (distance of hf) = (amount of B) x (distance of Bf)
(amount of B) = hf/Bh
(amount of liquid) = Bf/Bh
Liquid
B
(amount of B) = hf/Bh (amount of liquid) = Bf/Bh
Composition of liquid = h
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
Eutectic Reaction
Reactions at f point:
• T > T1 : 57% B (43%
liq.)
• T < T1 : 70% B (30% A)
mixture of A & B
crystallized
• The reaction described
above are those that
should occur under
equilibrium conditions.
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)
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 ?
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)
Phase diagram of CaO-SiO2 system
Immiscible Liquids
Formation of metastable 2-liquid system
It happens when “2-liquid  B + liquid” is very slow upon cooling
Binary system with complete range of
solid solution
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.
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
The plagioclase feldspar system
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.
Partial Solid Solution
If ions are quite different in size
 complete solid solution may not be possible.
e.g. forsterite (Mg2SiO4) vs willemite (Zn2SiO4)
Partial Solid Solution
A slightly complicated partial
solid solution
A complicated Partial Solid Solution
Binary system with polymorph transitions
example
Another example
The Fe-C diagram