Chapter 11: Phase Diagrams
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1 Chapter 11: 상태도 (Phase Diagrams) 학습목표 2 개의원소가결합이되면평형상태는어떤상태일까? 특히, 우리가다음과같은요소를정한다면.. -- 조성 (e.g., wt% Cu - wt% Ni), -- 온도 (T, temperature ) 몇개의상이형성될까? 각각의상은어떤조성이될까? 각각의상의양은얼마일까? Phase A Phase B Nickel atom Copper atom Chapter 11-1
2 Phase Equilibria: Solubility imit 용액 (Solution) 고체, 액체, 가스, 단일상 혼합물 (Mixture) 1개이상의상으로구성 용해한도 (Solubility imit): 단일상에서다른원소가존재할수있는최대조성 Q: 20 C 수용액에서설탕이녹을수있는용해한도는? Temperature ( C) Answer: 65 wt% sugar. At 20 C, if C < 65 wt% sugar: syrup At 20 C, if C > 65 wt% sugar: syrup + sugar Sugar/Water Phase Diagram Solubility imit (liquid solution i.e., syrup) (liquid) + S (solid sugar) C = Composition (wt% sugar) Water Adapted from Fig. 11.1, Callister & Rethwisch 9e. Sugar Chapter 11-2
3 성분과상 (Components and Phases) 성분 (Components) : 합금에존재하는원소또는화합물 (e.g., Al and Cu) 상 (Phases) : 물리적및화학적으로서로달리구성하고있는재료의영역 (e.g., and β). Aluminum- Copper Alloy Adapted from chapteropening photograph, Chapter 9, Callister, Materials Science & Engineering: An Introduction, 3e. β (lighter phase) (darker phase) Chapter 11-3
4 Temperature ( C) 100 조성과온도의영향 온도를변화하면상의개수는 : path A to B. 조성을변화하면상의개수는 : path B to D. watersugar system Fig. 11.1, Callister & Rethwisch 9e ( liquid solution i.e., syrup) B (100 C,C = 70) 1 phase (liquid) + S (solid sugar) C = Composition (wt% sugar) D (100 C,C = 90) 2 phases A (20 C,C = 70) 2 phases Chapter 11-4
5 고용도 ( Solid Solubility) 의기준 Simple system (e.g., Ni-Cu solution) 결정구조전기음성도 r (nm) Ni FCC Cu FCC 결정구조, 전기음성도, 원자반경이비슷할경우, 높은상호용해도를갖는다. (W. Hume Rothery rules) 니켈과구리는모든요소에서서로에대해완전히용해된다. Chapter 11-5
6 상태도 (Phase Diagrams) T, C, P 의함수로서상을나타냄.. 기본으로 : - 2 원계시스템 (binary systems): 2 개의성분으로구성. - 독립적변수 : 온도와조성 (T and C) (P = 1 atm 대기압. ) Phase Diagram for Cu-Ni system (liquid) (FCC solid solution) phases: (liquid) (FCC solid solution) 3 different phase fields: + Fig. 11.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, Reprinted by permission of ASM International, Materials Park, OH.) wt% Ni Chapter 11-6
7 전율고용 2원계상태도 Isomorphous Binary Phase Diagram 상태도 : Cu-Ni system. System is: -- 2 원계 (binary) i.e., 2 성분 : Cu and Ni. -- isomorphous i.e., 다른원소에대하여완전한용해도를보여주는상태 ; 0 ~ 100 wt% Ni 에서 상이연장된다 (liquid) (FCC solid solution) Fig. 11.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, Reprinted by permission of ASM International, Materials Park, OH.) Cu-Ni phase diagram wt% Ni Chapter 11-7
8 상태도 (Phase Diagrams): Rule 1: 온도 (T ) 와조성 (C o ) 를알면 : -- 상태도에서어떤상이존재할수있는지를정의할수있다. Examples: A(1100 C, 60 wt% Ni): 1 phase: B (1250 C, 35 wt% Ni): 2 phases: + Fig. 11.3(a), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, Reprinted by permission of ASM International, Materials Park, OH.) 존재하는상의정의 (liquid) B (1250ºC,35) (FCC solid solution) A(1100ºC,60) Cu-Ni phase diagram wt% Ni Chapter 11-8
9 Phase Diagrams: Determination of phase compositions Rule 2: If we know T and C 0, then we can determine: -- the composition of each phase. Examples: Consider C 0 = 35 wt% Ni At T A = 1320 C: Only iquid () present C = C 0 ( = 35 wt% Ni) At T D = 1190 C: Only Solid () present C = C 0 ( = 35 wt% Ni) At T B = 1250 C: Both and present C = C liquidus ( = 32 wt% Ni) C = C solidus ( = 43 wt% Ni) T A 1300 T B 1200 T D 20 (liquid) Cu-Ni system A B D 3235 tie line (solid) C C 0 C Fig. 11.3(b), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, Reprinted by permission of ASM International, Materials Park, OH.) wt% Ni Chapter 11-9
10 Phase Diagrams: Determination of phase weight fractions Rule 3: T 와 C 0 를정의하면 : -- 각상의질량비를정의할수있다. Examples: Consider C 0 = 35 wt% Ni T A 에서 : Only iquid () present W = 1.00, W = 0 T D 에서 : Only Solid ( ) present W = 0, W = 1.00 T B 에서 : W = W = Both and present S R + S R R + S = 0.27 T A 1300 T B 1200 T D 20 (liquid) Cu-Ni system A B R S D 3235 tie line (solid) 43 C C C 0 Fig. 11.3(b), Callister & Rethwisch 9e. (Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, Reprinted by permission of ASM International, Materials Park, OH.) wt% Ni Chapter 11-10
11 The ever Rule 타이라인 (Tie line) 서로열적평형상태의상을연결하는선 때로는등온선이라고도한다 T B 1200 (liquid) R B tie line S (solid) 각상의비율은? 지랫대법칙을생각하자. (teeter-totter) M M C C 0 C wt% Ni Adapted from Fig. 11.3(b), Callister & Rethwisch 9e. R S Chapter 11-11
12 Ex: Cu-Ni Alloy 의냉각 Phase diagram: Cu-Ni system. A 조성의합금에대하여냉각을동반미세구조변화를고려한다. C 0 = 35 wt% Ni alloy (liquid) 1300 : 35 wt% Ni : 46 wt% Ni (solid) A B C 24 D 36 E : 35 wt%ni Cu-Ni system : 32 wt% Ni : 43 wt% Ni : 24 wt% Ni : 36 wt% Ni : 35 wt% Ni Adapted from Fig. 11.4, Callister & Rethwisch 9e C 0 wt% Ni Chapter 11-12
13 기계적성질 : Cu-Ni System 고용강화 (solid solution strengthening) 에따른효과 : -- Tensile strength (TS) -- Ductility (%E) Tensile Strength (MPa) TS for pure Cu Cu Ni Composition, wt% Ni Adapted from Fig. 11.5(a), Callister & Rethwisch 9e. TS for pure Ni Elongation (%E) %E for pure Cu Cu Ni %E for pure Ni Composition, wt% Ni Adapted from Fig. 11.5(b), Callister & Rethwisch 9e. Chapter 11-13
14 2 원계공정시스템 (Binary-Eutectic Systems) 2 components Ex.: Cu-Ag system 3 개의단일상지역존재 (,, β) 제한된용해한도 : : mostly Cu β: mostly Ag T E : T E 이하에서는액상X C E : T E 에서의조성 has a special composition with a min. melting T 공정반응 (Eutectic reaction) (C E ) (C E ) + β(c βe ) cooling + (liquid) + β Cu-Ag system + β β T C E C E C, wt% Ag Fig. 11.6, Callister & Rethwisch 9e [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.]. heating Chapter 11-14
15 EX 1: Pb-Sn 공정상태도 150 C 에서 40 wt% Sn-60 wt% Pb alloy: 상을정의하시오. Answer: + β -- 각상의조성은? Answer: C = 11 wt% Sn C β = 99 wt% Sn -- 각상의상대적으로존재하는양은? Answer: S C W β - C 0 = = R+S C β - C = W β = = R = R+S = 59 = C 0 - C C β - C = 29 = C 18.3 R (liquid) + β Pb-Sn system + β C C 0 Fig. 11.7, Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in- Chief), Reprinted by permission of ASM International, Materials Park, OH.] S C, wt% Sn C β β Chapter 11-15
16 220 C 에서 40 wt% Sn-60 wt% Pb alloy: 상을정의하시오. Answer: + -- 각상의조성은? Answer: C = 17 wt% Sn C = 46 wt% Sn -- 각상의상대적으로존재하는양은? Answer: W = C - C 0 C - C = = 6 29 EX 2: Pb-Sn 공정상태도 = 0.21 W = C 0 - C C - C = = (liquid) 183 C + β Pb-Sn system + β C 0 C R S C Fig. 11.7, Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in- Chief), Reprinted by permission of ASM International, Materials Park, OH.] C, wt% Sn β Chapter 11-16
17 공정상태도를이용한 미세구조개발 I 예를들어, C 0 < 2 wt% Sn 결과적으로 : 실온에서는 -- 조성 C 0 를갖는 상이다결정으로존재한다 T E : C 0 wt% Sn : C 0 wt% Sn + (Pb-Sn System) β Fig , Callister & Rethwisch 9e. 0 C (room T solubility limit) 30 C, wt% Sn Chapter 11-17
18 공정상태도를이용한 미세구조개발 II 예를들어, 2 wt% Sn < C 0 < 18.3 wt% Sn Result: + β 의온도에서는 -- 결정립의다결정이생성되고작은 β- 상의입자들이석출된다 T E β : C 0 wt% Sn : C 0 wt% Sn β Pb-Sn system Fig , Callister & Rethwisch 9e C 0 (sol. limit at T room ) 18.3 (sol. limit at T E ) 30 C, wt% Sn Chapter 11-18
19 공정상태도를이용한 미세구조개발 III 합금조성이공정조성일때 (C 0 = C E ) 결과 : 공정미세구조를형성 (lamellar structure) -- 와 β 상이판상구조로교대로반복됨. 300 Pb-Sn system 200 T E C : C 0 wt% Sn + β β Micrograph of Pb-Sn eutectic microstructure Fig , Callister & Rethwisch 9e. + β β: 97.8 wt% Sn : 18.3 wt%sn C E C, wt% Sn 160 μm Fig , Callister & Rethwisch 9e. (From Metals Handbook, 9th edition, Vol. 9, Metallography and Microstructures, Reproduced by permission of ASM International, Materials Park, OH.) Chapter 11-19
20 amellar Eutectic Structure Figs & 11.14, Callister & Rethwisch 9e. (Fig from Metals Handbook, 9th edition, Vol. 9, Metallography and Microstructures, Reproduced by permission of ASM International, Materials Park, OH.) Chapter 11-20
21 공정상태도를이용한 미세구조개발 IV 예를들어, 18.3 wt% Sn < C 0 < 61.9 wt% Sn 결과 : 상의초정상와공정미세구조가형성된다. 300 Pb-Sn system 200 T E Fig , Callister & Rethwisch 9e. R R + β : C 0 wt% Sn S S + β C, wt% Sn β primary eutectic eutectic β T E 의바로위 : C = 18.3 wt% Sn C = 61.9 wt% Sn W S = = 0.50 R + S W = (1- W ) = 0.50 T E 의바로아래 : C = 18.3 wt% Sn C β = 97.8 wt% Sn S W = R + S = 0.73 W β = 0.27 Chapter 11-21
22 아공정 (Hypoeutectic) & 과공정 (Hypereutectic) Fig. 11.7, Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] T E β + β β (Pb-Sn System) (Figs and from Metals Handbook, 9th ed., Vol. 9, Metallography and Microstructures, Reproduced by permission of ASM International, Materials Park, OH.) hypoeutectic: C 0 = 50 wt% Sn μm Fig , Callister & Rethwisch 9e eutectic 61.9 eutectic: C 0 = 61.9 wt% Sn 160 μm eutectic micro-constituent Fig , Callister & Rethwisch 9e. C, wt% Sn hypereutectic: (illustration only) β β β β β Adapted from Fig , Callister & Rethwisch 9e. (Illustration only) β Chapter 11-22
23 중간화합물 (Intermetallic Compounds) Fig , Callister & Rethwisch 9e. [Adapted from Phase Diagrams of Binary Magnesium Alloys, A. A. Nayeb-Hashemi and J. B. Clark (Editors), Reprinted by permission of ASM International, Materials Park, OH.] Mg 2 Pb Note: 금속간화합물은상태도에라인으로존재한다 화학양론적조성이므로면이아님 - (i.e. 화합물의조성은고정값이다 ) Chapter 11-23
24 공석 (Eutectoid) 하나의고상은두개의다른고상으로변환 intermetallic compound S 2 S 1 +S 3 - cementite γ cool + Fe 3 C (For Fe-C, 727 C, 0.76 wt% C) heat 공정, 공석 & 포정 Eutectic, Eutectoid, & Peritectic 공정 (Eutectic): 액체는두개의고체상으로변환 cool + β (For Pb-Sn, 183 C, 61.9 wt% Sn) heat 포정 (Peritectic) - 액체및하나고체상이제 2 의고상으로변환 S 1 + S 2 cool δ + γ (For Fe-C, 1493 C, 0.16 wt% C) heat Chapter 11-24
25 Eutectoid & Peritectic Cu-Zn Phase diagram Peritectic transformation γ + δ Eutectoid transformation δ γ + ε Fig , Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 2, T. B. Massalski (Editor-in- Chief), Reprinted by permission of ASM International, Materials Park, OH.] Chapter 11-25
26 Iron-Carbon (Fe-C) 상태도 2 important points - Eutectic (A): γ + Fe 3 C - Eutectoid (B): γ + Fe 3 C 1600 δ γ γ + (austenite) B γ γ γ γ 1148 C A γ +Fe 3 C 727 C = T eutectoid +Fe 3 C +Fe 3 C Fe 3 C (cementite) 120 μm Result: Pearlite = alternating layers of and Fe 3 C phases Fig , Callister & Rethwisch 9e. (From Metals Handbook, Vol. 9, 9th ed., Metallography and Microstructures, Reproduced by permission of ASM International, Materials Park, OH.) (Fe) Fig , Callister & Rethwisch 9e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] C, wt% C Fe 3 C (cementite-hard) (ferrite-soft) Chapter 11-26
27 γ γ γ γ 아공석강 (Hypoeutectoid Steel) γ γ γ γ γ γ γ γ δ γ γ + (austenite) 727 C (Fe) C 0 C, wt% C pearlite C γ + Fe 3 C + Fe 3 C +Fe 3 C Fe 3 C (cementite) (Fe-C System) Adapted from Figs and 11.28, Callister & Rethwisch 9e. [Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] pearlite 100 μm Hypoeutectoid steel 초석페라이트 Adapted from Fig , Callister & Rethwisch 9e. (Photomicrograph courtesy of Republic Steel Corporation.) Chapter 11-27
28 γ γ γ γ W = s/(r + s) W γ =(1 - W ) 아공석강 (Hypoeutectoid Steel) δ W pearlite = W γ W = S/(R + S) γ γ + (austenite) r s R S 727 C pearlite (Fe) C W Fe 3 C =(1 W ) pearlite 1148 C γ + Fe 3 C + Fe 3 C +Fe 3 C C, wt% C Fe 3 C (cementite) (Fe-C System) 100 μm Hypoeutectoid steel Adapted from Figs and 11.28, Callister & Rethwisch 9e. [Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] 초석페라이트 Adapted from Fig , Callister & Rethwisch 9e. (Photomicrograph courtesy of Republic Steel Corporation.) Chapter 11-28
29 Fe 3 C 과공석강 (Hypereutectoid Steel) γ γ γ γ γ γ γ γ γ γ γ γ δ γ γ + (austenite) 727 C C (Fe) C 0 C, wt% C pearlite C γ + Fe 3 C + Fe 3 C +Fe 3 C Fe 3 C (cementite) (Fe-C System) Adapted from Figs and 11.31, Callister & Rethwisch 9e. [Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] pearlite 60 μm Hypereutectoid steel proeutectoid Fe 3 C Adapted from Fig , Callister & Rethwisch 9e. (Copyright 1971 by United States Steel Corporation.) Chapter 11-29
30 Fe 3 C γ γ γ γ W γ =x/(v + x) W =(1-W γ ) Fe 3 C W pearlite = W γ W = X/(V + X) δ W =(1 - W ) Fe 3 C 과공석강 (Hypereutectoid Steel) 800 γ γ + (austenite) V 727 C 600 pearlite + Fe 3 C C 0 (Fe) C v x pearlite X 1148 C γ + Fe 3 C +Fe 3 C C, wt% C Fe 3 C (cementite) (Fe-C System) 60 μm Hypereutectoid steel proeutectoid Fe 3 C Adapted from Figs and 11.31, Callister & Rethwisch 9e. [Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] Adapted from Fig , Callister & Rethwisch 9e. (Copyright 1971 by United States Steel Corporation.) Chapter 11-30
31 Example wt% Fe-0.40 wt% C 강은공석반응선바로밑에존재한다. 다음을정의하시오 : a) Fe 3 C 및 ferrite () 의조성은?. b) 100g 의강에서 cementite (Fe 3 C) 는몇 gram? c) 100g 의강에서 pearlite 및공석페라이트 () 는몇 gram? Chapter 11-31
32 Solution to Example Problem a) Using the RS tie line just below the eutectoid C = wt% C C Fe3 C = 6.70 wt% C b) 지랫대법칙사용 100 g 에서 Fe 3 C 의양 1600 δ γ γ + (austenite) R Fig , Callister & Rethwisch 9e. [From Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] 727 C 1148 C γ + Fe 3 C S + Fe 3 C +Fe 3 C Fe C (cementite) = (100 g)w Fe3 C = (100 g)(0.057) = 5.7 g C, wt% C C C 0 C Fe C 3 Chapter 11-32
33 Solution to Example Problem (cont.) c) Using the VX tie line just above the eutectoid and realizing that C 0 = 0.40 wt% C C = wt% C C pearlite = C γ = 0.76 wt% C 100 g에서의펄라이트양 = (100 g)w pearlite = (100 g)(0.512) = 51.2 g 1600 δ γ γ + (austenite) V X 727 C C C γ C, wt% C C 0 Fig , Callister & Rethwisch 9e. [From Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), Reprinted by permission of ASM International, Materials Park, OH.] 1148 C 공석페라이트 = 펄라이트양 Fe3C 의양 = = 45.6g 초석페라이트 = 전체페라이트 - 공석페라이트 = = 48.8 γ + Fe 3 C + Fe 3 C +Fe 3 C Fe C (cementite) Chapter 11-33
34 Alloying with Other Elements T eutectoid changes: C eutectoid changes: T Eutectoid (ºC) Ti Mo Ni Si W Cr Mn C eutectoid (wt% C) Ti Si Mo Ni Cr W Mn wt. % of alloying elements Fig , Callister & Rethwisch 9e. (From Edgar C. Bain, Functions of the Alloying Elements in Steel, Reproduced by permission of ASM International, Materials Park, OH.) wt. % of alloying elements Fig ,Callister & Rethwisch 9e. (From Edgar C. Bain, Functions of the Alloying Elements in Steel, Reproduced by permission of ASM International, Materials Park, OH.) Chapter 11-34
35 Summary 상태도 (Phase diagrams) 다음을결정하는데유용한데이터 : -- 존재하는상의종류및숫자, -- 각상의조성 ( composition), -- 각상의존재질량비 (weight fraction) ( 어떤시스템에서온도및조성주어진상태에서 ) 합금의미세구조에대한영향 -- 합금의조성 -- 열적평형상태를유지하는냉각속도의여부 상태도에서중요한상변태 (phase transformation) 는공정 (eutectic), 공석 (eutectoid) 그리고포정 (peritectic) 이다. Chapter 11-35
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