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Books to Refer
Materials Science
Phase Diagrams Dr. Renu Kumari Metallurgical and Materials Engineering National Institute of Technology (NIT) Jamshedpur 2
Why bother to Study Phase Diagrams? Phase Diagram?
It is the very reason that the life is protected ▪ It is a map that gives an initial idea on the evolution of phase(s) as a function of temperature, pressure and composition. Core of the Earth is Solid while the immediate Layer above it is Liquid?
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Types of Phase Diagrams Terminologies to Know (based on the number of components)
▪ Solute and Solvent? ▪ Components? ▪ Unary: Single Component Systems ▪ System? ▪ Degree of freedom? ▪ Binary: Two Components Systems ▪ ▪ Solubility limit? Variables? ▪ Ternary: Three Components Systems ▪ Equilibrium? ▪ Liquidus? ▪ Multi-components ▪ Phases? ▪ Solidus and Solvus?
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Variables in the Phase Diagrams Unary Phase Diagram
▪ Temperature H2O ▪ Pressure ▪ Composition
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Unary Phase Diagram Unary Phase Diagram
Iron (Fe) Iron (Fe)
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Binary Phase Diagram Binary Phase Diagrams Isomorphous System
▪ Complete solubility in the liquid as well as in the solid states. ▪ Isomorphous phase diagram ▪ Eutectic phase diagram
T 푇 ------L ------
푇 α
Awt % B B 11 (100 %) (100 %) 12
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Binary Phase Diagram Binary Phase Diagram Isomorphous System Isomorphous System
Complete mutual solubility Complete mutual solubility
Phase Identification Phase Identification
T T 푇 푇 L (1) 1-2-1 Rule L 1-2-1 Rule Phases between the boundaries Phases between the boundaries Tie Line Rule Phase composition 푇 α (1) 푇 α
Awt % B B Awt % B B (100 %) (100 %) 13 (100 %) (100 %) 14
Binary Phase Diagram Binary Phase Diagram Isomorphous System Isomorphous System
Cu-20% Ni Alloy How the phase evolves when heated to o Melting point? 1300oC and then cooled to room temperature?
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Binary Phase Diagram Isomorphous System
Assignments
1) The phase diagram for the cobalt–nickel system is an isomorphous one. On the basis of melting temperatures for these two metals, describe and/or draw a schematic sketch of the phase diagram for the Co–Ni system.
2) List a few other examples, preferably of practical importance, of Isomorphous systems. 3) List down the practical application/uses of the End of Lecture 1 isomorphous alloys listed and discussed.
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α β 퐶 − 퐶 퐶 − 퐶 Lever Rule Lever Rule 푓 = 푓 = 퐶 −퐶 퐶 −퐶 (Refer notes/books for derivation) CA C0 CB
Allows you to determine the fraction 푄1) 퐶표푚푝표푠푖푡푖표푛 표푓 푃ℎ푎푠푒푠? of phases from the phase diagram 푄2) 푓 = ?,푓 = ? α β
CA C0 CB
퐶 −퐶 푓 = 퐶 −퐶
퐶 −퐶 푓 = =1−푓 퐶 − 퐶
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α β 퐶 − 퐶 퐶 − 퐶 α β 퐶 − 퐶 퐶 − 퐶 Lever Rule 푓 = 푓 = Lever Rule 푓 = 푓 = 퐶 −퐶 퐶 −퐶 퐶 −퐶 퐶 −퐶 CA C0 CB CA C0 CB
푄1) 퐶표푚푝표푠푖푡푖표푛 표푓 푃ℎ푎푠푒푠? 푄1) 퐶표푚푝표푠푖푡푖표푛 표푓 푃ℎ푎푠푒푠?
푄2) 푓 = ?,푓 = ? 푄2) 푓 = ?,푓 = ?
C0 = 35 wt% Ni C0 = 35 wt% Ni
Cα = 42.5 wt% Ni Cα = 42.5 wt% Ni
CL = 31.5 wt% Ni CL = 31.5 wt% Ni
푓 = 0.68, 푓 = 0.32
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Binary Phase Diagram Binary Phase Diagram Isomorphous System Eutectic System
Phase Evolution
푇 L 푇 α β T
Awt % B B 23 (100 %) (100 %) 24
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Binary Phase Diagram Binary Phase Diagram Eutectic System Eutectic System
푇 푇 L L 푇 푇 α β α β T T
α + β α + β
Awt % B B Awt % B B (100 %) (100 %) 25 (100 %) (100 %) 26
Binary Phase Diagram Binary Phase Diagram Eutectic System Eutectic System
Eutectic Reaction Pb-Sn Eutectic Reaction 퐿 ⇄ 훼 + 훽 퐿 ⇄ 훼 + 훽 푇 L 푇 Lowest melting point Lowest melting point α β T
α + β
Awt % B B (100 %) (100 %) 27 28
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Binary Phase Diagram Binary Phase Diagram Eutectic System Eutectic System Eutectic Reaction 퐿 ⇄훼 + 훽 (Lowest melting temperature) (Lowest melting temperature)
NaCl-H2O Eutectic Reaction Pb-Sn Pb- 40 wt%Snalloy at 150°C(300°F): 퐿 ⇄ 퐼푐푒 +푆푎푙푡 (a) Whatphase(s)is(are)present? (b) What is (are) the composition(s) of 0o Why ice melts below C if Salt is the phase(s)? spread over the Ice? (c) Calculate the relative amount of phases
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Binary Phase Diagram Eutectic System Eutectic Reaction 퐿 ⇄훼 + 훽 (Lowest melting temperature) Gibbs Phase Rule (Refer notes/books for derivation)
Pb-Sn Pb - 40 wt% Sn alloy at 150°C (300°F): P+F=C+N P = number of phases (a) Whatphase(s)is(are)present? F = degree of freedom (T, P, X) (b) What is (are) the composition(s) of C = number of components the phase(s)? N = number of non-compositional variables (T, P) (c) Calculate the relative amount of phases
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Gibbs Phase Rule Invariant Reaction
P+F=C+N F=0 P = number of phases F = degree of freedom (T, P, X) C = number of components N = number of non-compositional variables (T, P, X)
Binary Phase Diagram F = 3 - P
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Fe-Fe3C Phase Diagram (metastable) T
End of Lecture 2
35 36 Fewt % C Fe3C
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Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable) T T
37 38 Fewt % C Fe3C Fewt % C Fe3C
Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable) T T
39 40 Fewt % C Fe3C Fewt % C Fe3C
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Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable)
훿 퐿 T 훾
훼
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Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable)
Invariant Reactions Invariant Reactions 훿 퐿 훿 퐿 F = 0; Three phases at equilibrium F = 0; Three phases at equilibrium
훾 훾 훿+퐿⇄훾
퐿 ⇄ 훾 + 퐹푒 퐶
훼 훼 훾 ⇄ 훼 + 퐹푒 퐶
43 44 Fewt % C Fe3C Fewt % C Fe3C
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Invariant Reaction Fe-Fe3C Phase Diagram (metastable)
F=0
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Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable)
Ferrite Pearlite
Austenite 훾⇄훼+퐹푒 퐶 Hypo-eutectoid/eutectic
Hyper-eutectoid/eutectic 푓 = ?
푓 = ?
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Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable)
Pearlite Ledeburite
훾⇄훼+퐹푒 퐶 퐿 ⇄ 훾 + 퐹푒 퐶
푓 = 88 % 푓 = ? 푓 = 12 % 푓 = ?
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Experimental Methods? Assignments
Available in the notes and refer books Available online
Try to solve first
We can have another dedicated session to discuss specific questions/issues/confusions
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End of Lecture 3
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