Ternary Systems # 1
11/15/2005
Ternary Phase Diagrams • Three component systems A, B and C • requires that we know the three binary systems for the 3 components – AB, BC, CA
• Ternary diagrams present a map of the Liquidus surface which is contoured with respect to Temperature. • Fields indicated on the ternary diagram represent the primary phase fields present on the Liquidus surface. Brock University
©2001 G.C. Finn
Ternary Diagrams - First Step T8
T8
Liquid
T7
Liquid
Liquid
T7
T6
T6
B+L
B+L
T5
C+L T5
e2
A+L
C+L A+L
T4
e1 T3
T3
B+C
A+B
T4
e3 C+A
T2
T2
T1
T1
B
A
B
C
C
A
Each Ternary diagram is constructed using the three binary diagrams for the three components AB, BC and CA Brock University
©2001 G.C. Finn
Ternary Diagrams - First Step T8
T8
Liquid
T7
Liquid
Liquid
T7
T6
T6
B+L
B+L
C+L
T5
T5
e2
A+L
C+L A+L
T4
e1 T3
T3
B+C
A+B
e3 C+A
T2
T1
A
T4
T2
T1
BB
CC
A
Each Ternary diagram is constructed using the three binary diagrams for the three components AB, BC and CA Brock University
©2001 G.C. Finn
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Ternary Systems # 1
11/15/2005
Ternary Diagrams - Next Step T8
T7
T6
T5
T4
e3
e2 T3
e1 T2
e3 E
A
T1
C The projection of the three
e1
e2 dimensional liquidus
E
surface onto the base of the triangle to present a twodimensional view of the surface.
B Brock University
©2001 G.C. Finn
Ternary Diagrams
e3
A
C e1
B
e2
E
Last Step
B A copy of the base of the triangle onto which the liquidus surface has been projected, showing the location of the binary eutectics (e1, e2, e3) and the ternary eutectic (E).
e2
E The projected surface above rotated into an upright position and stretched out into an equilateral triangle.
e1
A
C
e3
Brock University
©2001 G.C. Finn
Ternary Diagrams As we are looking at a map of the liquidus surface, we must have a solid and liquid in equilibrium. The shaded area shows where solid B and Liquid are in equilibrium
The edge of the triangle joining A and e1 B is an Alkemade Line, as the two phases A and B share a boundary curve, from e1 to E.
B
Phase Fields Cotectic Lines or Boundary Curves Alkemade Lines
B+L
e2
E
Cotectic Line or Boundary Curve separates two phase field from each other
A+L C+L
A Brock University
e3
C ©2001 G.C. Finn
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Ternary Systems # 1
11/15/2005
Ternary Diagrams
At Point 1, which lies in the field C + L
B
Phase Rule
P = 2 - Solid C and L
P+F=C+1
C = 3 - A, B and C F=2
At E, all three phase fields meet;
At Point 2, which lies on the Boundary Curve separating the fields of A + L from B + L;
B+L
P = 3 - Solid A, Solid B and L
P = 4 - Solid A, Solid B, Solid C and L C = 3 - A, B and C
e2
E
F=0
e1
C = 3 - A, B and C
2
F=1
1
A+L C+L
C
e3
A Brock University
©2001 G.C. Finn
Compositions in Ternary Diagrams • All compositions e.g. bulk compositions, liquid compositions, solid compositions on ternary diagrams are expressed in terms of the three end-member components which define the system. • These are located at the apices of the triangle.
Brock University
©2001 G.C. Finn
Ternary Compositions
B
The components (A, B and C) which define a ternary diagram are placed at the apices of the triangle.
10
At the apex there exists 100% of that component, with the percentage decreasing away from the apex, such that the side of the triangle opposite the apex represents 0% of that component.
90
20
80
30
50
%
Inc rea sin g
60
50
g sin rea Inc
%
A
70
40
60
B
40
70
30
80
20
90
A
10
10
20
30
40
50
60
70
80
90
C
Increasing % C Brock University
©2001 G.C. Finn
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Ternary Systems # 1
11/15/2005
Ternary Compositions • Compositions of points which lie inside a ternary diagram can be determined by using either of two methods: – Triangular Grid – Two Line Method
Brock University
©2001 G.C. Finn
Triangular Grid Method • In this method a series of grid lines are constructed. • The proportion of any point within the triangle can be represented by grid lines drawn through the point of interest, parallel to each side of the triangle. B
Composition 1
10
90
20
80
30
20% A 70
40
60% B
60
1
50
50
60
20% C 40
70 80
20
90
A
100% Total
30
10
10
20
30
40
50
60
70
80
C
90
Brock University
©2001 G.C. Finn
Two Line Method In this method two lines are drawn through the composition point of interest, parallel to any two sides of the triangle.
Composition 1 20% A
%C
60% B 20% C 100% Total
The two lines are parallel to the AB and AC sides of the triangle and intersect along the BC side, dividing this side into three line segments.
B
%A 1
The lengths of the individual line segments are proportional to the relative amounts of the three components A, B and C.
%B
A Brock University
C ©2001 G.C. Finn
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Ternary Systems # 1
11/15/2005
Ternary Compositions The two methods used to determine compositions were applied to an equilateral triangle. However, both methods can be applied to scalene triangles. To work with scalene triangles the “triangular grid” (Method 1) and the “two lines” (Method 2) must be drawn parallel to the edges of the scalene triangle.
B
B Method 1 - Triangular Grid Method
%C
%A
1 1
%B
C
A Method 2 - Two Line Method
C
A
Brock University
©2001 G.C. Finn
Ternary Compositions B
Determine the compositions of the points in the following table. %A
%B
%C
E 1
B+L
2 e3
e2
E
e1
1 2 A+L
A Brock University
e3
C+L
C ©2001 G.C. Finn
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