9 장상태도 (Phase Diagrams) 배워야할주요내용 상평형이란? 1성분계상태도 2성분계상태도 : 전율고용체, 공정계 상태도읽는법, 활용하는법 철-탄소상태도 1
상相 [Phase] 동일한구조와원자배열 동일한조성 인접상과뚜렷한계면 - 물리적으로구분가능 기계적으로분리가능 A phase is a homogeneous, physically distinct, mechanically separable portion of a material with a given chemical composition and structure. 2
상률 [Phase Rule] The Gibbs Phase Rule F + P = C + 2 F: 자유도 (degree of Freedom, 변수의수 ) P: 상의수 C: 성분 (component) 의수 성분이란? - 계를독립적으로구성하고있는원자, 분자, 화합물의수 3
상평형 [Phase Equilibrium] 주어진외부조건에서최소의자유에너지를가질때, 평형이이루어졌다고함. 일반적으로 - 기계적평형 ( 압력 ) - 열적평형 ( 온도 ) - 화학적평형 ( 화학포텐셜, 조성 ) 모두가이루어졌을때평형이라고할수있음. 4
1 성분계상태도 [Single component phase diagram] 각영역들에대해 Gibbs 의상률을적용하여보라! Invariant Univariant Bivarinat Trivariant(?) 5
용액과혼합물, 고용체 6
용액과혼합물, 고용체 용액 : ( 용질 + 용매 ), A + B = C 예, 소금 + 물 = 소금물 Cu + Zn = Brass ( 황동 ) 혼합물 : (A + B) = (A + B) 예, 모래 + 물 = 모랫물 (?) 고용체 : 고체용매안에고체용질이녹아있는고체용액 7
무한용해도의조건 Hume-Rothery 법칙 크기요소 : 용질과용매원자반경차이가 15% 이하. 결정구조 : 동일한결정구조일것. 원자가 : 동일한원자가일것. 전기음성도 : 거의동일한전기음성도일것. 고용체가아닌화합물형성 8
2 성분계상태도 [Binary component phase diagram] 전율고용체 (Complete Solid Solution) 전조성범위에서용해도를갖는고용체, Hume-Rothery 법칙을잘만족시키는고용체 9
Cu-Ni 2 원계상태도 ( 전율고용체 system) 액상선과고상선 각영역의자유도는? (Gibbs 의상률적용 ) 무변수반응은어디? T( C) 1600 1500 1400 1300 1200 1100 1000 0 L (liquid) (FCC solid solution) 20 40 60 80 100 2 phases: L (liquid) (FCC solid solution) 3 phase fields: L L + Adapted from Fig. 9.3(a), Callister 7e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH (1991). wt% Ni 10
상태도읽기 : 상의개수와종류 Rule 1: 온도와조성이주어지면상태도상에서상의개수와종류를알수있다! 예 : A(1100 C, 60): 1 phase: B(1250 C, 35): 2 phases: L + T( C) 1600 1500 1400 1300 1200 L (liquid) B (1250 C,35) (FCC solid solution) Cu-Ni phase diagram Adapted from Fig. 9.3(a), Callister 7e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991). 1100 1000 0 A(1100 C,60) 20 40 60 80 100 wt% Ni 11
상태도읽기 : 상의조성 Rule 2: 온도와조성이주어지면상태도상에서각상들의조성을알수있다! ( 공액선법칙 =Tie-line Principle) 예 : Co = 35 wt% Ni At T A = 1320 C: Only Liquid (L) CL = Co ( = 35 wt% Ni) At T D = 1190 C: Only Solid ( ) C = Co ( = 35 wt% Ni) At T B = 1250 C: T( C) TA 1300 TB 1200 TD 20 Both and L CL = Cliquidus ( = 32 wt% Ni here) C = Csolidus ( = 43 wt% Ni here) L (liquid) A B D 3235 C L C o tie line (solid) 4 3 C 30 40 50 wt% Ni Adapted from Fig. 9.3(b), Callister 7e. (Fig. 9.3(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 12
예 : 상태도읽기 : 공존하는상의상대양 Rule 3: 온도와조성이주어지면상태도상에서공존하는각상들의상대양을알수있다! ( 지렛대법칙 =Lever Rule) Co = 35 wt% Ni At T A: Only Liquid (L) WL = 100 wt%, W = 0 At T D: Only Solid ( ) At T B: W L = W = WL = 0, W = 100 wt% Both and L S R +S R R +S = 43 43 35 32 = 27 wt% = 73 wt% T( C) TA 1300 TB 1200 TD 20 L (liquid) A B R S D 3235 C L C o tie line (solid) 4 3 C 30 40 50 wt% Ni Adapted from Fig. 9.3(b), Callister 7e. (Fig. 9.3(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 13
평형냉각과정의미세조직변화 T( C) 1300 L: 35 wt% Ni : 46 wt% Ni 1200 L (liquid) 35 32 (solid) A B C D 24 36 E L: 35wt%Ni 43 46 Cu-Ni system L: 32 wt% Ni : 43 wt% Ni L: 24 wt% Ni : 36 wt% Ni 110 0 20 Adapted from Fig. 9.4, Callister 7e. 35 Co 30 40 50 wt% Ni 14
유핵 (Cored) 조직과평형조직 비평형응고 ( 상변태 ) 에의한편석 급냉 (Fast rate of cooling): 유핵조직 (Cored structure) 최초응고한 46 wt% Ni 마지막으로응고한 < 35 wt% Ni 서냉 (Slow rate of cooling): 평형 (Equilibrium) 조직 균일조성의 35 wt% Ni 15
고용체형성에따른기계적물성변화 고용강화효과 Tensile Strength (MPa) 400 300 TS for pure Cu 200 0 20 40 60 80 100 Cu Ni TS for pure Ni Composition, wt% Ni Elongation (%EL) 20 0 20 40 60 80 100 Cu Ni Composition, wt% Ni Adapted from Fig. 9.6(a), Callister 7e. Adapted from Fig. 9.6(b), Callister 7e. 60 50 40 30 %EL for pure Cu %EL for pure Ni 16
Cu-Ag system 3 개의단상영역 (L,, β) 제한된고용도 : : Cu-rich β: Ag-rich T E : 온도 T E 위에서모두액상 C E : 가장낮은융점의조성 2 성분계공정상태도 공정 (Eutectic) 반응 L(C E ) (C E ) + β(c βe ) T( C) 1200 1000 600 400 200 0 L + L (liquid) + β L+β β T 800 779 C E 8.0 71.9 91.2 C E 20 40 60 80 100 C o, wt% Ag Adapted from Fig. 9.7, Callister 7e. 17
공정상태도의미세조직변화 : I T( C) 400 300 L: C o wt% Sn L L 200 T E : C o wt% Sn L + (Pb-Sn System) Adapted from Fig. 9.11, Callister 7e. 100 + β 0 10 C o 2 (room T solubility limit) 20 30 C o, wt% Sn 18
공정상태도의미세조직변화 : II 400 T( C) L: C o wt% Sn 300 200 L L + L : C o wt% Sn Adapted from Fig. 9.12, Callister 7e. T E β 100 + β Pb-Sn system 0 10 20 2 C o (sol. limit at T room ) 18.3 (sol. limit at T E ) 30 C o, wt% Sn 19
공정상태도의미세조직변화 : III 공정조성의미세조직 = 층상조직 (lamellar structure) 300 Pb-Sn system 200 T E T( C) L L+ 183 C L: C o wt% Sn L + β β 100 + β β: 97.8 wt% Sn : 18.3 wt%sn 160 µm Adapted from Fig. 9.14, Callister 7e. 0 Adapted from Fig. 9.13, Callister 7e. 20 40 60 80 100 18.3 C E 97.8 61.9 C, wt% Sn 20
층상공정조직 Adapted from Figs. 9.14 & 9.15, Callister 7e. 21
공정상태도의미세조직변화 : IV 300 Pb-Sn system 200 T E 100 T( C) 0 L+ R R +β Adapted from Fig. 9.16, Callister 7e. L: C o wt% Sn L L L S 20 40 60 80 100 18.3 61.9 97.8 S L+β C o, wt% Sn β primary eutectic eutectic β 공정온도바로위의온도 : C = 18.3 wt% Sn C L = 61.9 wt% Sn S W= = 50 wt% R + S W L = (1- W) = 50 wt% 공정온도바로아래온도 : C = 18.3 wt% Sn Cβ = 97.8 wt% Sn S W= = 73 wt% R + S Wβ = 27 wt% 22
아공정과과공정조성의미세조직 Hypoeutectic & Hypereutectic Adapted from Fig. 9.8, Callister 7e. (Fig. 9.8 adapted from Binary Phase Diagrams, 2nd ed., Vol. 3, T.B. Massalski (Editor-in- Chief), ASM International, Materials Park, OH, 1990.) 300 T( C) 200 T E 100 L+ L + β L+β β (Pb-Sn System) (Figs. 9.14 and 9.17 from Metals Handbook, 9th ed., Vol. 9, Metallography and Microstructures, American Society for Metals, Materials Park, OH, 1985.) hypoeutectic: C o = 50 wt% Sn 0 175 µm Adapted from Fig. 9.17, Callister 7e. 20 40 60 80 100 eutectic 61.9 eutectic: C o = 61.9 wt% Sn 160 µm eutectic micro-constituent Adapted from Fig. 9.14, Callister 7e. C o, wt% Sn hypereutectic: (illustration only) β β β β β Adapted from Fig. 9.17, Callister 7e. (Illustration only) β 23
2 성분계상태도의 3 상공존반응 24
포정상태도 [Peritectic] 25
포정합금의미세조직변화 26
편정상태도 [Monotectic] 27
철 - 탄소 (Iron-Carbon, Fe-C) 상태도 2 개의중요반응 - 공정 (A): L γ + Fe 3 C - 공석 (B): γ +Fe 3 C 1600 δ 1400 1200 1000 800 600 T( C) γ γ+l (austenite) R B γ γ γ γ 1148 C R L A γ+fe 3 C 727 C = Teutectoid S +Fe 3 C L+Fe 3 C S Fe 3 C (cementite) 120 µm 펄라이트 (Pearlite) = 와 Fe 3 C 의층상조직 (Adapted from Fig. 9.27, Callister 7e.) 400 0 1 2 3 4 5 6 6.7 (Fe) 0.76 C eutectoid 4.30 Fe 3 C (cementite-hard) (ferrite-soft) Adapted from Fig. 9.24,Callister 7e. C o, wt% C 28
아공석강 (Hypoeutectoid Steel) 1600 δ 1400 1200 1000 800 600 T( C) γ γ+l (austenite) 727 C 1148 C 400 0 (Fe) C 0 1 2 3 4 5 6 6.7 pearlite w pearlite = wγ w =S/(R+S) =(1-w) w Fe3 C γ γ γ γ γ γ γ γ γ γ γ γ w =s/(r+s) wγ =(1- w) r s R S 0.76 pearlite L γ + Fe 3 C + Fe 3 C Adapted from Fig. 9.30,Callister 7e. L+Fe 3 C Fe 3 C (cementite) C o, wt% C (Fe-C System) 100 µm Hypoeutectoid steel Adapted from Figs. 9.24 and 9.29,Callister 7e. (Fig. 9.24 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in- Chief), ASM International, Materials Park, OH, 1990.) proeutectoid ferrite 29
Fe 3 C γ γ γ γ γ γ γ γ γ γ γ γ 과공석강 (Hypereutectoid Steel) 1600 δ 1400 1200 1000 800 T( C) γ γ+l (austenite) 1148 C 600 w Fe3 C =r/(r +s) +Fe 3 C wγ =(1-w Fe3 C) 400 0 1 C o 2 3 4 5 6 6.7 pearlite (Fe) C o, wt%c w pearlite = wγ w =S/(R+S) w Fe3 C =(1-w ) R 0.76 r s pearlite S L γ +Fe 3 C L+Fe 3 C Fe 3 C (cementite) (Fe-C System) 60 µm Hypereutectoid steel proeutectoid Fe 3 C Adapted from Figs. 9.24 and 9.32,Callister 7e. (Fig. 9.24 adapted from Binary Alloy Phase Diagrams, 2nd ed., Vol. 1, T.B. Massalski (Ed.-in- Chief), ASM International, Materials Park, OH, 1990.) Adapted from Fig. 9.33,Callister 7e. 30
탄소강에첨가하는합금원소의영향 공석온도를변화 공석조성을변화 TEutectoid ( C) Ti Mo Ni Si W Cr Mn Ceutectoid (wt%c) Ti Si Mo Ni Cr W Mn wt. % of alloying elements Adapted from Fig. 9.34,Callister 7e. (Fig. 9.34 from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 127.) wt. % of alloying elements Adapted from Fig. 9.35,Callister 7e. (Fig. 9.35 from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 127.) 31