Periodic Table
INGE 4001 - Engineering Materials
Chapter
p 10
Solid Solutions and Phase
Equilibrium
Periodic Table
INGE 4001 - Engineering Materials
Phase Diagram Basics
• What is a phase?
• A phase
h
di
diagram represents
t
P=3
what phases are present at a
ggiven ppressure,, temperature
p
and
composition.
• Virtual maps of equilibrium
conditions in a system.
• Gibb’s phase rule: 2 + C = P + F
• There are 2 thermodynamic
variables: temperature and
pressure.
pressure
P=1
P=2
Periodic Table
INGE 4001 - Engineering Materials
Phase Diagrams of Pure Substances – Unary Phase Diagrams
Pressure-Temperature phase diagram of pure water
At one
atmosphere of
pressure there are
two phases
changes at 0ºC
and 100ºC
Let’s apply the phase rule to
g of this diagram
g
each region
What is a
supercritical
iti l fluid?
fl id?
Periodic Table
INGE 4001 - Engineering Materials
The Clausius-Clapeyron Equation:
dp
ΔH
=
dT T ⋅ ΔV
•The equation applies to any two phases α and β (solid, liquid
or gaseous).
gaseous)
• Remember L is positive for melting and apply the equation to
water.
water
Periodic Table
INGE 4001 - Engineering Materials
P-T
P
T Phase Diagram of Pure Iron
At 1 atm. there are three
phase changes at 910ºC,
1394ºC and 1538ºC
Remember that iron
is a polymorphic
metal
Periodic Table
INGE 4001 - Engineering Materials
Other P-T Phase Diagrams of Pure Substances
Carbon unary phase diagram: Note
the extension of the graphite region.
What does it mean?
CO2 phase diagram: Note
that on the mp line: dP/dT is
positive
Periodic Table
INGE 4001 - Engineering Materials
• Thermal
Th
l analysis
l i of:f
– Phase transformations
– Solidification
– Precipitation
• Cooling curves analysis
• Construction of binary phase
diagrams using thermocouples
Periodic Table
mV
Handheld
thermocouple
Read tthis webpaage:
http://ww
ww.omega.com/therm
mocoupless.html
Cooling Curve Determination (pages 315-316)
INGE 4001 - Engineering Materials
Construction of a Binary
Phase Diagram
Each curve was collected
during cooling
cooling.
Note the beginning and end of
each thermal event
(transformation).
They correlate with one point in
the phase diagram below.
This is an isomorphous
system
Apply the phase rule on
each portion of the curves
INGE 4001 - Engineering Materials
Periodic Table
Isomorphous
p
System
y
• A system with complete solubility in
solid state.
• One solid phase a is stable from one
end to the other of the system.
• Remember the four conditions for
solid solubility by Hume-Rothery.
Solidification
• Examples: Cu-Ni, Ag-Au, NiO-MgO,
NiO-CoO, Ge-Si, GaAs-InAs.
Homework: find at least three more systems
(you always
(y
y need to to pprovide the
references)
INGE 4001 - Engineering Materials
Periodic Table
Cu-Ni is an example of an isomorphous
system
Z
Crystal
St
Structure
t
electronegativity
r (nm)
28
FCC
1.9
0.1246
Cu 29
FCC
1.8
0.1278
Ni
• Both have the same crystal structure (FCC)
( CC) and have
similar electronegativities and atomic radii (W. Hume –
y rules)) suggesting
gg
g high
g mutual solubility
y
Rothery
• Ni and Cu are totally miscible in all proportions
Periodic Table
INGE 4001 - Engineering Materials
Cu-Ni Phase Diagram
Two key questions: (I) What is the chemical composition of all phases present for
alloy X at temperature T?
(II) What is the relative amount of all phases present for alloy X
att temperature
t
t T?
Periodic Table
INGE 4001 - Engineering Materials
Chemical Composition and
Relative Amount of Phases Present at 1250ºC
1250 C
Liquid
Li
id contains
t i 32 wt.%
t % α solid
lid solution
l ti contains
t i 45
wt.% Ni and 55 wt.% Cu
Ni and 68 wt.% Cu
INGE 4001 - Engineering Materials
Periodic Table
Relative Amount of Phases Present at 1250ºC
In erse Le
Inverse
Lever
er R
Rule
le
%α =
40 − 32
⋅ 100
45 − 32
% a = 61.5 %
% Liq =
Periodic Table
45 − 40
⋅ 100 % Liq = 39.5 %
45 − 32
INGE 4001 - Engineering Materials
Composition Change During Solidification
Composition of first
Composition
C
iti off llastt
solid a to form
liquid to solidify
Wh t is
What
i th
the composition
iti off th
the llastt solid
lid to
t fform??
Periodic Table
INGE 4001 - Engineering Materials
Weight Percent and
Atomic Percent
Why is there such a
difference between
both scales?
Other
Example:
Sb-Bi
Periodic Table
INGE 4001 - Engineering Materials
Weight Percent and Atomic Percent
Conversion Formulas
wt.%A
atomic weight
eight of A
at.%A =
wt.%A
wt.%B
+
atomic weight of A atomic weight of B
For the at.%B just replace A for B in the numerator
(at.%A ) ⋅ (atomic weight
g of A )
wt.%
%A =
(at.%A ) ⋅ (atomic weight of A ) + (at.%B) ⋅ (atomic weight of B)
For the wt.%B just replace A for B in the numerator
So, for the GeGe-Si phase diagram by just looking at the scales you
should be able to tell which element has a higher atomic weight
INGE 4001 - Engineering Materials
Periodic Table
Other examples
p of isomorphous
p
pphase diagrams
g
GaAs-InAs System
1300
Al2O3 – Cr2O3 System
aGaAs=0.566 nm
1250
Temperature (ºC)
1200
1150
1100
1050
1000
950
aInAs=0.606
0 606 nm
900
850
800
0
10
20
30
40
50
60
mol.% InAs
70
80
Semiconductors
Periodic Table
90
100
Hard Ceramics
INGE 4001 - Engineering Materials
One variation of isomorphous systems presents a minima
Ti-Zr
partial
phase
diagram
Still there are a liquidus line and a solidus line. In this case they meet
i th
in
three points:
i t bboth
th melting
lti points
i t andd th
the minima.
i i
Periodic Table
INGE 4001 - Engineering Materials
Solubility Revisited
• What is solubility?
• How does is change
g with temperature?
p
• Phase diagrams provides information of
solubility.
solubility
Hume-Rothery
Rothery
• Again: remember the Hume
rules for solid solubility prediction
Periodic Table
INGE 4001 - Engineering Materials
Let’s use the solubility concept The solubility limit line is the
t something
to
thi we like:
lik sugar
location of all the saturation
points at different
temperatures. Another
example:
These are partial phase diagrams!!
Periodic Table
INGE 4001 - Engineering Materials
Chapter 11
Dispersion
p
Strengthening
g
g
and Eutectic Phase
Diagrams
Periodic Table
INGE 4001 - Engineering Materials
When soluble
Wh
l bl substances
b t
suddenly become insoluble
i t eachh other…
into
th
Let’s
L
t’ llearn h
how tto read
these phase diagrams.
Think of winter in Alaska.
Alaska
This lowest melting points are
called eutectics
Periodic Table
INGE 4001 - Engineering Materials
And With Partial Solubility in Solid State…
Eutectic point
Max. solubility of
Cu in the Ag
lattice
Periodic Table
Max. solubility of
Ag in the Cu
lattice
INGE 4001 - Engineering Materials
Solidification of Ag-Sn Eutectic Alloy
T
How many phases are
present at each
temperature
p
for this
alloy? Degrees of
freedom?
time
Periodic Table
INGE 4001 - Engineering Materials
Solidification of a Hypereutectic Ag-Sn Alloy
T
time
Apply the phase rule on each portion of this curve
Periodic Table
INGE 4001 - Engineering Materials
Eutectic Reactions (cont.)
• Eutectic reactions are special cases of
invariant or isothermal reactions ((F = 0))
• Eutectic reactions can be described with
the follo
following
ing form
formula:
la
Li id ' Solid
Liquid
S lid 1 + S
Solid
lid 2
att T
T= Teut
INGE 4001 - Engineering Materials
Periodic Table
More on Partial Solubility Diagrams
INGE 4001 - Engineering Materials
Periodic Table
Sn-Pb Alloyy Microstructures at Different Compositions
p
Eutectic
Composition
63% Sn
S - 37% Pb
Hypoeutectic
Composition
40% Sn
S - 60% Pb
Hypereutectic
Composition
70 % Sn – 30 % Pb
Hypereutectic
yp
Composition
90 % Sn – 10 % Pb
Compositions are in weight percent
Periodic Table
INGE 4001 - Engineering Materials
Periodic Table
INGE 4001 - Engineering Materials
Eutectics
• They have very interesting morphologies.
• They are due to a cooperative growth
Look at the atoms moving ahead
of the solidification front.
Simulation of solute redistribution
during binary eutectic growth.
4001 - Engineering Materials
Non-EquilibriumINGE
Solidification
in Eutectic Systems
Periodic Table
For normal solidification to occur we need fast diffusion of solute (Sn in this
case)) iin th
the recently
tl fformedd solid.
lid IIn thi
this system
t andd others
th (Al
(Al-Cu,
C etc.)
t ) this
thi
doesn’t occur
Sn (solute) atoms are
rejected into the
remaining liquid.
The actual composition
of the liquid nears the
eutectic.
The segregation
g g
in the
α phase is called
“coring.”
Can you foresee any
problem in using this
microseggregated
alloy?