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Materials Science (MM1201)-PD 4/16/2020 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? 3 4 1 4/16/2020 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? 5 6 Variables in the Phase Diagrams Unary Phase Diagram ▪ Temperature H2O ▪ Pressure ▪ Composition 7 8 2 4/16/2020 Unary Phase Diagram Unary Phase Diagram Iron (Fe) Iron (Fe) 9 10 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 3 4/16/2020 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? 15 16 4 4/16/2020 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. 17 18 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 19 20 5 4/16/2020 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 21 22 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 6 4/16/2020 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 7 4/16/2020 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 29 30 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 31 32 8 4/16/2020 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 33 34 Fe-Fe3C Phase Diagram (metastable) T End of Lecture 2 35 36 Fewt % C Fe3C 9 4/16/2020 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 10 4/16/2020 Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable) 훿 퐿 T 훾 훼 41 42 Fewt % C Fe3C Fewt % C Fe3C 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 + 퐹푒퐶 훼 훼 훾 ⇄ 훼 + 퐹푒퐶 43 44 Fewt % C Fe3C Fewt % C Fe3C 11 4/16/2020 Invariant Reaction Fe-Fe3C Phase Diagram (metastable) F=0 45 46 Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable) Ferrite Pearlite Austenite 훾⇄훼+퐹푒퐶 Hypo-eutectoid/eutectic Hyper-eutectoid/eutectic 푓 = ? 푓 = ? 47 48 12 4/16/2020 Fe-Fe3C Phase Diagram (metastable) Fe-Fe3C Phase Diagram (metastable) Pearlite Ledeburite 훾⇄훼+퐹푒퐶 퐿 ⇄ 훾 + 퐹푒퐶 푓 = 88 % 푓 = ? 푓 = 12 % 푓 = ? 49 50 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 51 52 13 4/16/2020 End of Lecture 3 53 14.
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