Isoplethal Analysis of a Ternary Phase Diagram

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Isoplethal Analysis of a Ternary Phase Diagram

• Presented By
• Adam Chamberlain

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Definitions

• Primary Crystallization Field
• Gives the first solid that forms upon cooling

• Compatibility Triangle
• Gives the final solid mixture of the composition

• Crystallization Path
• The path that is followed upon cooling a liquid.
  The path that is traced gives the composition of
  the liquid while cooling the solid composition
  is determined using tie lines from the liquid
  path.

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Isoplethal Analysis
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Finding the composition
C

• Method of Parallel lines

Alkemade lines
B
Ltotal length
Given a composition X A, Y B, ZC
Boundary lines
E2
A
E1
C ZC x L

• Draw a line parallel to AB

C
A
B
AXA x L
AB
composition

• Draw a line parallel to AC

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The 3 questions
C

• What is the primary crystallization field?

• The field is AB

• What is the compatibility triangle?

E2
E1

• C-AB-B

• What is the invariant point?

• To find the invariant point, locate the point
  within the diagram that has each of the
  components of the compatibility triangle in
  equilibrium, in this case E2

A
B
AB
Alkemade lines
Boundary lines
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Crystallization Path
C

• Draw a line connecting the composition to the
  composition of the crystallization field

• Continue the line until it hits a boundary line

E2
E1

• Follow the boundary line until the invariant
  point is reached

A
B
AB
final liquid composition
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Analysis at T1

• Above T1 only liquid is present

C

• The composition of the liquid is found using
  parallel lines

• Below T1 an infinitesimal amount of AB
  crystallizes.

E2

• Percent solid and liquid is given by the tie line

E1
T1

• Percent A and B in AB is given by the tie line ab

y
A
B
a
AB
b
Temp Prop Phase
Composition Analysis

A
B C
T1() 100 L
(L)Parallel Lines 100A
100B 100C
T2() y/yL 100L (L)
same 100A
100B 100C e
0S (S) 100AB
0100A 0100B

Aa/ab Bb/ab
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Analysis at T2
C

• Above T2 there is solid AB and liquid.

• Percent solid and liquid is given by the tie line
  xy

E2

• The liquid composition is found using parallel
  lines method at T2

E1
T2
x
y

• Below T2 infinitesimal amount of B crystallizes

A
B
a
AB
b
Temp Prop Phases
Composition
Analysis

A B
C
T2 () Ly y/xyL
(L)parallel lines LA
LB LC
Sx x/xyS
(S)100AB SABA
SABB
Aa/ab Bb/ab
T2(-) same same
(L)same LA
LB LC
(S)
100AB 0B SABA SABBSB

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Analysis above TE
C

• Above TE solid AB, B, and liquid are present

• Percent solid and liquid are given by the tie
  line xy

E2

• Liquid composition is given using parallel lines
  method

E1
x

• Percent AB and B are given by the tie line ab and
  b

y
A
B
AB
b
ab
Temp Prop Phases
Composition
Analysis A B
C
TE() Ly y/xyL
(L)parallel lines LA
LA LC Lx
x/xyS (S) a/abAB
SABA SABB

b/abB
SB
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Analysis below TE
C

• Below TE only solid is present

AB

• The composition is given by using the parallel
  lines method at the initial composition with
  respect to its compatibility triangle

E2
E1
B
C
A
B
AB
Temp Prop Phases
Composition
Analysis

A B
C
TE 100 S
parallel lines
100ABA 100ABB 100C


100A
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Analysis of the KF-NaF-MgF2 System

• Identify boundary lines

• Identify the Alkemade lines

• Identify the compatibility triangles

NaFMgF2- MgF2- KFMgF2
NaFMgF2- NaF- KFMgF2
Alkemade lines
NaF- KFMgF2- 2KFMgF2
Boundary lines
NaF- 2KFMgF2-KF
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Locating the composition

• 17NaF-23MgF2-60KF

KF
NaF 100 x .17 17
MgF2 100 x .23 23
MgF2
NaF
Triangle sides are 100 mm
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The 3 questions

• What is the primary crystallization field?

E
KFMgF2

• What is the compatibility triangle?

NaF-2KFMgF2-KF

• What is the invariant point?

E
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Crystallization Path

• Draw a line connecting the composition to the
  composition of the primary crystallization field

• Continue the line until it hits the boundary line

• KFMgF2 is resorbed to form all 2KFMgF2 at 750

• The line is then extended to the boundary of NaF
  and 2KFMgF2

• The boundary line is then followed until the
  eutectic reaction is reached

Crystallization Path
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Analysis at 850

• Above 850 only liquid is present

• The composition is given by the initial
  composition

• Below 850 an infinitesimal amount of KFMgF2
  crystallizes

• Percent solid and liquid are given by the tie
  line y

y
Temp Prop Phases
Composition
Analysis
MgF2 KF NaF
850 () 100L
(L) 17NaF 23MgF2 60KF 17
23 60

850(-) y23 100L (L)
same 17 23
60 e
0S (S)100 KFMgF250KF 50MgF2
010050 010050
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Analysis at 780

• Above 780 there is liquid and solid KFMgF2
  present

• Percent solid and liquid are given by the tie
  line xy

• Liquid composition is found using parallel lines
  at 780

x

• Below 780 KFMgF2 is being resorbed to form
  2KFMgF2

y
Temp Prop Phases
Composition
Analysis MgF2
KF NaF
780() y 23 82 L
(L) 22 NaF 16 MgF2 62 KF
13 51
18 x 5 18 S
(S) 100 KFMgF2
9
9
780() same same
(L) same
13 51
18 same
same (S) 100 KFMgF2
0 2KFMgF2 9
9
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Analysis at 750

• At 750 resorption is complete and the solid is
  100 2KFMgF2

• The liquid composition is found using parallel
  lines

x
y
Temp Prop Phases
Composition
Analysis
MgF2
KF NaF
750 y 15 56 L
(L)32NaF 12 MgF2 53KF
7 30
18 Resorption x 12 44 S
(S)100 2KFMgF2 67KF 33MgF2 15
30 complete

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Analysis at 700

• Since all KFMgF2 is resorbed the path proceeds
  through the 2KFMgF2 crystallization field

• Above 700 liquid and solid 2KFMgF2 are present

• Percent liquid and solid are given by the tie
  line xy

x
y

• Below 700 infinitesimal amount NaF crystallizes

Temp Prop Phases
Composition
Analysis
MgF2 KF NaF
700() y 15 45 L
(L) 39NaF 10 MgF2 51 KF 5
23 17
x 18 55 S (S)
100 2KFMgF2
18 37
700(-) same same
(L) same
5 23
17
(S) 100 2KFMgF2
0 NaF 18
37 0
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Analysis above 685

• Above 650 solid NaF, 2KFMgF2, and liquid are
  present

2KFMgF2

• Percent solid and liquid are given by the tie
  line xy

x

• The solid composition is found by using the
  NaF-2KFMgF2 Alkemade line as a tie line

y
NaF
Temp Prop Phases
Composition
Analysis MgF2
KF NaF
685() y 6 27 L
(L) 34NaF 6 MgF2 60 KF 2
16
9 x 16 73 S
(S) 13 NaF 21
43 9
87 2KFMgF2
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Analysis Below 650

• Below 650 the eutectic reaction takes place

2KFMgF2

• 100 solid is present

• The composition is found using parallel lines
  through the original composition with respect to
  the compatibility triangle

KF
NaF
Temp Prop Phases
Composition
Analysis MgF2
KF NaF
650(-) 100 S
(S) 20 NaF
21 16
20

16 KF
43

64 2KFMgF2
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Summary

• First identify the important features of the
  phase diagram Alkemade and boundary lines,
  invariant points, etc.

• Locate the composition on the diagram

• Determine the crystallization path

• Finally, perform the analysis