This slide set corresponds to the MaterialsConcepts YouTube video "Muddiest Point- Phase Diagrams I: Eutectic Calculations and Lever Rule ". Here is the link: http://www.youtube.com/watch?v=h5dwpTqacqc To study the vocab used in this video, visit this site: http://quizlet.com/20699402/51-phase-diagram-concepts-and-terms-flash-cards/ This work was supported by NSF Grants #0836041 and #1226325.

1. Muddiest
Points
Phase
Diagram
I:
Calcula7ons
&
Lever
Rule
Muddiest
Points:
•
What
do
alpha
and
beta
represent?
• What
is
the
eutec7c
reac7on?
•
How
do
I
find
chemical
composi7on
and
phase
frac7on
from
a
phase
diagram?

2. Eutectic Phase Diagram Terminology
Liquidus
L
α+L
Eutec1c
Reac1on
α β +
L
TEu
β
Solidus
Solubility
limit
α + β
Solubility
limit
of
Sn
in
α
of
Pb
in
β
CEu
Hypoeutec7c
Comp.
Hypereutec7c
Comp.
(Pb)
Composi7on
(wt.
%
Sn)
(Sn)

3. L
Eutectic Reaction in the Pb-Sn Phase Diagram
S1
+
S2
Liquidus
General
Eutec7c
Reac7on
L
Temp
Reac7on
L
a
S1
+
S2
α+L
Eutec1c
Reac1on
Comp.
L
Comp
S1
Comp
S2
α β +
L
TEu
β
Sol
limit
of
B
in
S1
Solidus
Sol
limit
of
A
in
S2
Solubility
limit
α + β
Solubility
limit
Pb
-­‐
Sn
Eutec7c
Reac7on
of
Sn
in
α
of
Pb
in
β
183
C
L
a
α
+
β
61.9%Sn
18.3%Sn
97.8%Sn
CEu
Hypoeutec7c
Comp.
Hypereutec7c
Comp.
(Pb)
Composi7on
(wt.
%
Sn)
(Sn)

4. Phase
Calcula7ons
For
40
wt%
Sn
-­‐
60
wt%
Pb
(Co
)
at
150°C
1)
phases
present:
2)
Chemical
comp
of
each
phase:
Co
L
T
(°C)
Cα
Cβ
α+L
Eutec7c
Rx
α β +
L
3)
Phase
wt.
frac.
(0
a1)
of
each
ph.:
β
Q Cβ-­‐Co
150
Wα=
Q
P+Q
Cβ-­‐Cα
P
α + β
P
Co-­‐Cα
11
%
40%
61.9%
99
%
Wβ=
P+Q
Cβ-­‐Cα
Cα
Co
CEu
Cβ
(Pb)
Composi7on
(wt.
%
Sn)
(Sn)

5. 6012$'*1@%"@1&542'
!"#$!%&!'()!*+!,!-&!'()!./!0!!!!1!2(!34&56!
*5'
!!-.!/012$2'/3$2$4#7!
N.'*0$DE%1@'%5D/!#9!:2;<!=<2>:7!
*5' +EI"EJ'
L
G'AH*.'
*!#
*"# !++' !"#$%&%' ()'
! " ,'+''
K.'6012$'F#?'L31%?'A9'!-.'5L'$1%0'/0?M' "
'
7 *":*5' -89''
8!=# 7
6,7' *":*!# 6'
! + "#
6' *5:*!' --'<' ;9<' >-?=<' =='<'
8"=# 6,7'
*":*!# *!# *5' *!"' *"#
A6B.' *5D/52E&54'AF#?'<'C4.''' AC4.'
Given
1)
150C;
2)
40Sn-­‐60Pb
(2-­‐phase
region)

6. Muddiest
Points
Phase
Diagram
I:
Calcula7ons
&
Lever
Rule
Muddiest
Points:
•
What
do
alpha
and
beta
represent?
• What
is
the
eutec7c
reac7on?
•
How
do
I
find
chemical
composi7on
and
phase
frac7on
from
a
phase
diagram?