Chpter 9: 상태도 (Phse Digrms) ISSUES TO ADDRESS... When we combine two elements... wht is the resulting equilibrium stte? In prticulr, if we specify... -- the composition (e.g., wt% Cu - wt% Ni), nd -- the temperture (T ) then... How mny phses form? Wht is the composition of ech phse? Wht is the mount of ech phse? Phse A Phse B Nickel tom Copper tom Chpter 9-1
Wter Sugr Temperture (ºC) 상평형 (Phse Equilibri): 용해한도 (Solubility imit) 고용체 고체, 액체, 기체상의단상으로구성 혼합 한상이상으로구성 용해한도 (Solubility imit): 단상으로구성하는용매에용해되는용질의최대농도 Question: 20ºC 에서물에대한설탕의용해한도는? 10 0 8 0 6 0 4 0 20 Answer: 65 wt% sugr. 20ºC, C < 65 wt% sugr: syrup 20ºC, C > 65 wt% sugr: syrup + sugr Sugr/Wter Phse Digrm Solubility imit (liquid solution i.e., syrup) Adpted from Fig. 9.1, Cllister & Rethwisch 8e. (liquid) + S (solid sugr) 0 20 40 6065 80 100 C = Composition (wt% sugr) Chpter 9-2
성분과상 (Components nd Phses) 성분 (components): 합금을구성하는순금속이나화합물 (e.g., Al nd Cu) 상 (phses): 물리적 화학적특성이균일한계의균질한부분 (e.g., nd b). Aluminum- Copper Alloy Adpted from chpteropening photogrph, Chpter 9, Cllister, Mterils Science & Engineering: An Introduction, 3e. b (lighter phse) (drker phse) Chpter 9-3
Temperture (ºC) 100 온도와조성의영향 온도 (T) 의변화 상의변화 : pth A to B. 조성 (C) 의변화 상의변화 : pth B to D. wtersugr system Adpted from Fig. 9.1, Cllister & Rethwisch 8e. 80 60 40 20 0 0 ( liquid solution i.e., syrup) B (100ºC,C = 70) 1 phse (liquid) + S (solid sugr) 20 40 60 70 80 100 C = Composition (wt% sugr) D (100ºC,C = 90) 2 phses A (20ºC,C = 70) 2 phses Chpter 9-4
고용체의기준 (Criteri for Solid Solubility) 단순계 (e.g., Ni-Cu solution) Crystl Structure electroneg r (nm) Ni FCC 1.9 0.1246 Cu FCC 1.8 0.1278 두가지모두같은결정구조 (FCC), 유사한전기음성도와원자반경 (W. Hume Rothery rules) 는높은상호고용도를예측할수있음 Ni 와 Cu 는모든조성에서서로완전한용해도를보임 Chpter 9-5
상태도 (Phse Digrms) T, C와 P에따른상 (phse) 구분 본강의에서 : - 2원계 (binry systems): 2가지성분으로구성 - 독립변수 : 온도 (T) 와성분 (C) (P = 1 tm, 대기압 ) Phse Digrm for Cu-Ni system 1600 1500 1400 1300 1200 1100 1000 0 (liquid) (FCC solid solution) 20 40 60 80 100 2 phses: (liquid) (FCC solid solution) 3 가지다른상영역 : + Adpted from Fig. 9.3(), Cllister & Rethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of Binry Nickel Alloys, P. Nsh (Ed.), ASM Interntionl, Mterils Prk, OH (1991). wt% Ni Chpter 9-6
전율고용 2원계상태도 (Isomorphous Binry Phse Digrm) Phse digrm: Cu-Ni system. System is: -- 2원계 (binry) i.e., 2가지조성 : 1400 Cu와 Ni 1300 -- 전율고용체 (isomorphous) i.e., 두성분이액상과고상에서서로완전한용해도를갖음 ; phse field extends from 0 to 100 wt% Ni. 1600 1500 1200 1100 1000 0 (liquid) (FCC solid solution) 20 40 60 80 100 Cu-Ni phse digrm wt% Ni Adpted from Fig. 9.3(), Cllister & Rethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of Binry Nickel Alloys, P. Nsh (Ed.), ASM Interntionl, Mterils Prk, OH (1991). Chpter 9-7
Phse Digrms: 상의종류결정 Rule 1: T 와 C o 를알면 : -- 존재하는상 (phse(s)) 의종류를알수있다. Exmples: A(1100ºC, 60 wt% Ni): 1 phse: B (1250ºC, 35 wt% Ni): 2 phses: + Adpted from Fig. 9.3(), Cllister & Rethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of Binry Nickel Alloys, P. Nsh (Ed.), ASM Interntionl, Mterils Prk, OH (1991). 1600 1500 1400 1300 1200 1100 1000 0 (liquid) B (1250ºC,35) (FCC solid solution) A(1100ºC,60) 20 40 60 80 100 Cu-Ni phse digrm wt% Ni Chpter 9-8
Phse Digrms: 상의조성결정 Rule 2: T 와 C o 를알면 : -- 개개상의조성을알수있다. Exmples: C 0 = 35 wt% Ni의조성 T A = 1320ºC: 액상 () 만이존재 C = C 0 ( = 35 wt% Ni) T D = 1190ºC: 고상 () 만이존재 C = C 0 ( = 35 wt% Ni) T B = 1250ºC: 두상 와 이존재 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) 43 30 40 50 C C 0 C wt% Ni Adpted from Fig. 9.3(), Cllister & Rethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of Binry Nickel Alloys, P. Nsh (Ed.), ASM Interntionl, Mterils Prk, OH (1991). Chpter 9-9
Rule 3: T 와 C o 를알면 : -- 개개상의무게분율를알수있다. Exmples: C 0 = 35 wt% Ni T A : 액상 () 만이존재 W = 1.00, W = 0 T D : 고상 ( ) 만이존재 Phse Digrms: 상의무게분율 ( 양 ) 결정 W = 0, W = 1.00 T B : 두가지 와 존재 W S R + S W R R + S 43 43 = 0.27 35 32 0.73 T A 1300 T B 1200 T D 20 (liquid) Cu-Ni system A B R S D 3235 tie line (solid) 43 C 30 40 50 C C 0 wt% Ni Adpted from Fig. 9.3(), Cllister & Rethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of Binry Nickel Alloys, P. Nsh (Ed.), ASM Interntionl, Mterils Prk, OH (1991). Chpter 9-10
지렛대원리 (The ever Rule) 공액선 (Tie line) 평형상태에서 2 상구역내각상의경계선과연결 등온선 (isotherm) 1300 T B 1200 (liquid) R B tie line S (solid) 각상의분율은? 공액선 (tie line) 을지렛대로간주 (lever) (teeter-totter 혹은 see-sw) M M 20 30 C 40 50 C 0 C wt% Ni Adpted from Fig. 9.3(b), Cllister & Rethwisch 8e. R S M x S M x R W M M M S R S C C C0 C W R R S C C 0 C C Chpter 9-11
Ex: Cu-Ni Alloy 의냉각 상태도 : Cu-Ni system. C 0 = 35 wt% Ni lloy의냉각에따르는미세조직의변화 1300 : 35 wt% Ni : 46 wt% Ni 120 0 (liquid) 35 32 (solid) A B C 24 D 36 E : 35wt%Ni 43 46 Cu-Ni system : 32 wt% Ni : 43 wt% Ni : 24 wt% Ni : 36 wt% Ni 110 0 20 Adpted from Fig. 9.4, Cllister & Rethwisch 8e. 35 30 40 50 C 0 wt% Ni Chpter 9-12
느린냉각속도 : 평형조직 유핵 vs 평형조직 (Cored vs Equilibrium Structures) 냉각에따른 C 의조성변화 Cu-Ni 의경우 : 최초고상 의조성 C = 46 wt% Ni. 최종고상 의조성 C = 35 wt% Ni. Uniform C : 35 wt% Ni 빠른냉각속도 : 유핵조직 First to solidify: 46 wt% Ni st to solidify: < 35 wt% Ni Chpter 9-13
Tensile Strength (MP) Elongtion (%E) 고용체강화의영향 : 기계적성질 : Cu-Ni System -- Tensile strength (TS) -- Ductility (%E) 400 300 TS for pure Cu 200 0 20 40 60 80 100 Cu Ni Composition, wt% Ni Adpted from Fig. 9.6(), Cllister & Rethwisch 8e. TS for pure Ni 60 50 40 30 %E for pure Cu 20 0 20 40 60 80 100 Cu Ni %E for pure Ni Composition, wt% Ni Adpted from Fig. 9.6(b), Cllister & Rethwisch 8e. Chpter 9-14
2 가지조성 Ex.: Cu-Ag system 3 개의단일상구역 (,, b) 제한된용해도 : : 대부분 Cu b: 대부분 Ag T E : T E 이하액상무 C E : 온도 T E 에서의조성 2 원공정계 (Binry-Eutectic Systems) 1200 1000 600 400 200 0 공정반응 (Eutectic rection) 최소의용해온도 (T) 를갖는특정조성 + (C E ) (C E ) + b(c be ) cooling (liquid) b Cu-Ag system Adpted from Fig. 9.7, Cllister & Rethwisch 8e. + b b T 800 779ºC E 8.0 71.9 91.2 20 40 60 80 100 ( 71.9 wt% Ag) (8.0 wt% Ag) b(91.2 wt% Ag) heting C E C, wt% Ag Chpter 9-15
150ºC 에서 40 wt% Sn-60 wt% Pb lloy: -- 존재하는상 Pb-Sn Answer: + b system -- 상의조성 Answer: C = 11 wt% Sn C b = 99 wt% Sn -- 각상의분율 Answer: W = S C b - C = 0 R+S C b - C = W b = = 99-40 99-11 R = R+S 40-11 99-11 EX 1: Pb-Sn 공정계 = 59 = 0.67 88 C 0 - C C b - C = 29 88 = 0.33 300 200 150 100 0 + 183ºC 18.3 R (liquid) + b + b 61.9 97.8 11 20 40 60 80 99100 C C 0 Adpted from Fig. 9.8, Cllister & Rethwisch 8e. S C, wt% Sn C b Chpter 9-16 b
220ºC 에서 40 wt% Sn-60 wt% Pb lloy: -- 존재상 : Pb-Sn Answer: + system -- 상조성 Answer: C = 17 wt% Sn C = 46 wt% Sn -- 각상의분율 Answer: W = C - C 0 C - C = = 6 29 = 0.21 W = C 0 - C = 23 C - C 29 EX 2: Pb-Sn 공정계 46-40 46-17 = 0.79 300 220 200 100 0 + (liquid) 183ºC + b + b 17 20 40 46 60 80 100 C 0 C R Adpted from Fig. 9.8, Cllister & Rethwisch 8e. S C C, wt% Sn Chpter 9-17 b
공정계의미세조직 I C 0 < 2 wt% Sn 의합금 결과 : 상온 -- C 0 의조성을갖는 phse 결정으로구성된다결정 400 300 200 T E : C 0 wt% Sn : C 0 wt% Sn + (Pb-Sn System) 100 + b Adpted from Fig. 9.11, Cllister & Rethwisch 8e. 0 C 0 10 20 2 (room T solubility limit) 30 C, wt% Sn Chpter 9-18
공정계의미세조직 II 2 wt% Sn < C 0 < 18.3 wt% Sn 합금 결과 : + b 구역내의온도 -- grins 과작은 b-phse 입자를갖는다결정 400 300 200 T E 100 + + b : C 0 wt% Sn : C 0 wt% Sn b Pb-Sn system Adpted from Fig. 9.12, Cllister & Rethwisch 8e. 0 10 20 2 C 0 (sol. limit t T room ) 18.3 (sol. limit t T E ) 30 C, wt% Sn Chpter 9-19
공정합금의미세조직 III 합금의조성 : C 0 = C E 결과 : 공정합금미세조직, 층상구조 (lmellr structure) -- 와 b 상의층상 (lmelle) 구조 300 Pb-Sn system 200 T E + 183ºC : C 0 wt% Sn b b Microgrph of Pb-Sn eutectic microstructure 100 b b: 97.8 wt% Sn : 18.3 wt%sn 160 m Adpted from Fig. 9.14, Cllister & Rethwisch 8e. 0 Adpted from Fig. 9.13, Cllister & Rethwisch 8e. 20 40 60 80 100 18.3 C E 97.8 61.9 C, wt% Sn Chpter 9-20
mellr Eutectic Structure Adpted from Figs. 9.14 & 9.15, Cllister & Rethwisch 8e. Chpter 9-21
공정계의미세조직 IV 18.3 wt% Sn < C 0 < 61.9 wt% Sn 결과 : 상입자와공정형미세구성인자 300 Pb-Sn system 200 T E 100 0 + R R + b Adpted from Fig. 9.16, Cllister & Rethwisch 8e. : C 0 wt% Sn S 20 40 60 80 100 18.3 61.9 97.8 S + b C, wt% Sn b primry eutectic eutectic b T E 직상 : C = 18.3 wt% Sn C = 61.9 wt% Sn S W = = 0.50 R + S W = (1- W ) = 0.50 T E 직하 : C = 18.3 wt% Sn C b = 97.8 wt% Sn W S = = 0.73 R + S W b = 0.27 Chpter 9-22
아공석 (Hypoeutectic) & 공석 (Hypereutectic) Adpted from Fig. 9.8, Cllister & Rethwisch 8e. (Fig. 10.8 dpted from Binry Phse Digrms, 2nd ed., Vol. 3, T.B. Msslski (Editor-in-Chief), ASM Interntionl, Mterils Prk, OH, 1990.) (Figs. 9.14 nd 9.17 from Metls Hndbook, 9th ed., Vol. 9, Metllogrphy nd Microstructures, Americn Society for Metls, Mterils Prk, OH, 1985.) 300 200 T E 100 0 + hypoeutectic: C 0 = 50 wt% Sn 175 m Adpted from Fig. 9.17, Cllister & Rethwisch 8e. + b + b 20 40 60 80 100 eutectic 61.9 eutectic: C 0 = 61.9 wt% Sn 160 m eutectic micro-constituent Adpted from Fig. 9.14, Cllister & Rethwisch 8e. b (Pb-Sn System) C, wt% Sn hypereutectic: (illustrtion only) b b b b b b Adpted from Fig. 9.17, Cllister & Rethwisch 8e. (Illustrtion only) Chpter 9-23
금속간화합물 (Intermetllic Compounds) Adpted from Fig. 9.20, Cllister & Rethwisch 8e. Mg 2 Pb Note: 금속간화합물은상태도에선으로표시- 면적이아님 정해진화학식을갖음 (i.e. 화합물의조성이정해짐 ). Chpter 9-24
공정 (Eutectic), 공석 (Eutectoid), & 포정 (Peritectic) Eutectic 액상이 2개의고상으로상변화 cool + b (Pb-Sn의경우, 183ºC, 61.9 wt% Sn) het Eutectoid 1개의고상이 2개의다른고상으로상변화 금속간화합물 - cementite S 2 S 1 +S 3 cool + Fe 3 C (Fe-C의경우, 727ºC, 0.76 wt% het C) Peritectic 액상과고상이다른 1개의고상으로상변화 S 1 + S 2 cool + (Fe-C 의경우, 1493ºC, 0.16 wt% C) het Chpter 9-25
Eutectoid & Peritectic Cu-Zn Phse digrm Peritectic trnsformtion + Eutectoid trnsformtion + Adpted from Fig. 9.21, Cllister & Rethwisch 8e. Chpter 9-26
Fe 3 C (cementite) 철 - 탄소 (Fe-C) 상태도 2 중요한 points - Eutectic (A): + Fe 3 C - Eutectoid (B): + Fe 3 C 1600 1400 1200 1000 800 + (ustenite) B 1148ºC A +Fe 3 C 727ºC = T eutectoid +Fe 3 C 600 +Fe 3 C 120 m Result: Perlite = lternting lyers of nd Fe 3 C phses (Adpted from Fig. 9.27, Cllister & Rethwisch 8e.) 400 0 1 2 3 4 5 6 6.7 (Fe) 0.76 Adpted from Fig. 9.24, Cllister & Rethwisch 8e. 4.30 C, wt% C Fe 3 C (cementite-hrd) (ferrite-soft) Chpter 9-27
0.76 Fe 3 C (cementite) 아공석강 (Hypoeutectoid Steel) 1600 1400 1200 1000 800 600 + (ustenite) 400 0 1 2 3 4 5 6 6.7 (Fe) perlite C 0 727ºC 1148ºC + Fe 3 C + Fe 3 C +Fe 3 C C, wt% C (Fe-C System) 100 m Hypoeutectoid steel Adpted from Figs. 9.24 nd 9.29,Cllister & Rethwisch 8e. (Fig. 9.24 dpted from Binry Alloy Phse Digrms, 2nd ed., Vol. 1, T.B. Msslski (Ed.-in- Chief), ASM Interntionl, Mterils Prk, OH, 1990.) perlite Adpted from Fig. 9.30, Cllister & Rethwisch 8e. proeutectoid ferrite Chpter 9-28
0.76 Fe 3 C (cementite) W = s/(r + s) W =(1 - W ) 1600 1400 1200 1000 800 600 W perlite = W W = S/(R + S) 아공석강 (Hypoeutectoid Steel) + (ustenite) r perlite 400 0 1 2 3 4 5 6 6.7 (Fe) C 0 s R S W Fe 3 C =(1 W ) perlite 727ºC 1148ºC + Fe 3 C + Fe 3 C +Fe 3 C C, wt% C Adpted from Fig. 9.30, Cllister & Rethwisch 8e. (Fe-C System) 100 m Hypoeutectoid steel Adpted from Figs. 9.24 nd 9.29,Cllister & Rethwisch 8e. (Fig. 9.24 dpted from Binry Alloy Phse Digrms, 2nd ed., Vol. 1, T.B. Msslski (Ed.-in- Chief), ASM Interntionl, Mterils Prk, OH, 1990.) proeutectoid ferrite Chpter 9-29
0.76 Fe 3 C (cementite) Fe 3 C 과공석강 (Hypereutectoid Steel) 1600 1400 1200 1000 800 600 + (ustenite) 400 0 1 2 3 4 5 6 6.7 (Fe) perlite C 0 1148ºC +Fe 3 C +Fe 3 C +Fe 3 C C, wt%c (Fe-C System) Adpted from Figs. 9.24 nd 9.32,Cllister & Rethwisch 8e. (Fig. 9.24 dpted from Binry Alloy Phse Digrms, 2nd ed., Vol. 1, T.B. Msslski (Ed.-in-Chief), ASM Interntionl, Mterils Prk, OH, 1990.) perlite 60 m Hypereutectoid steel proeutectoid Fe 3 C Adpted from Fig. 9.33, Cllister & Rethwisch 8e. Chpter 9-30
0.76 Fe 3 C (cementite) Fe 3 C W =x/(v + x) W =(1-W ) Fe 3 C W perlite = W W = X/(V + X) 1600 1400 1200 1000 W =(1 - W ) Fe 3 C 과공석강 (Hypereutectoid Steel) 800 + (ustenite) 600 perlite +Fe 3 C 400 0 1 2 3 4 5 6 6.7 (Fe) V v C 0 x perlite X 1148ºC +Fe 3 C +Fe 3 C C, wt%c (Fe-C System) 60 m Hypereutectoid steel proeutectoid Fe 3 C Adpted from Figs. 9.24 nd 9.32,Cllister & Rethwisch 8e. (Fig. 9.24 dpted from Binry Alloy Phse Digrms, 2nd ed., Vol. 1, T.B. Msslski (Ed.-in-Chief), ASM Interntionl, Mterils Prk, OH, 1990.) Adpted from Fig. 9.33, Cllister & Rethwisch 8e. Chpter 9-31
예제 99.6 wt% Fe-0.40 wt% C 강에대하여공석점직하의온도에서다음을결정하라 : ) Fe 3 C 와 ferrite () 의조성 b) 100 g 의강중 cementite (in grms) 의양 c) 100 g 중 perlite 와 proeutectoid ferrite () 의양 Chpter 9-32
Fe C (cementite) W Fe 3 C R R S Solution to Exmple Problem ) 공석점직하에서 RS tie line 을이용 C = 0.022 wt% C C Fe3 C = 6.70 wt% C b) tie line 에서지렛대원리이용 C 0 C C Fe 3 C C 0.40 0.022 6.70 0.022 0.057 100 g 중 Fe 3 C 의양 1600 1400 1200 1000 800 600 (ustenite) R + 727ºC 1148ºC + Fe 3 C S + Fe 3 C +Fe 3 C = (100 g)w Fe3 C = (100 g)(0.057) = 5.7 g 400 0 1 2 3 4 5 6 6.7 C, wt% C C C 0 Chpter 9-33 C Fe C 3
Fe C (cementite) Solution to Exmple Problem (cont.) c) 공석점직상의온도에서 VX tie line 를이용 W perlite C 0 = 0.40 wt% C C = 0.022 wt% C C perlite = C = 0.76 wt% C V V X C 0 C C C 0.40 0.022 0.76 0.022 0.512 100 g 중 perlite 의양 1600 1400 1200 1000 800 600 (ustenite) V X + 1148ºC + Fe 3 C 727ºC + Fe 3 C +Fe 3 C = (100 g)w perlite = (100 g)(0.512) = 51.2 g 400 0 1 2 3 4 5 6 6.7 C C C, wt% C C 0 Chpter 9-34
VMSE: Interctive Phse Digrms Microstructure, phse compositions, nd phse frctions respond interctively Chnge lloy composition Chpter 9-35
T Eutectoid (ºC) C eutectoid (wt% C) Alloying with Other Elements T eutectoid chnges: C eutectoid chnges: Ti Mo Si W Ni Cr Ni Cr Mn Ti Si Mo W Mn wt. % of lloying elements Adpted from Fig. 9.34,Cllister & Rethwisch 8e. (Fig. 9.34 from Edgr C. Bin, Functions of the Alloying Elements in Steel, Americn Society for Metls, 1939, p. 127.) wt. % of lloying elements Adpted from Fig. 9.35,Cllister & Rethwisch 8e. (Fig. 9.35 from Edgr C. Bin, Functions of the Alloying Elements in Steel, Americn Society for Metls, 1939, p. 127.) Chpter 9-36
Summry Phse digrms re useful tools to determine: -- the number nd types of phses present, -- the composition of ech phse, -- nd the weight frction of ech phse given the temperture nd composition of the system. The microstructure of n lloy depends on -- its composition, nd -- whether or not cooling rte llows for mintennce of equilibrium. Importnt phse digrm phse trnsformtions include eutectic, eutectoid, nd peritectic. Chpter 9-37
ANNOUNCEMENTS Reding: Core Problems: Self-help Problems: Chpter 9-38