Chapter 9: Phase Diagrams

Transcription

1 Chpter 9: 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

2 Wter Sugr Temperture (ºC) Phse Equilibri: Solubility imit Solution solid, liquid, or gs solutions, single phse Mixture more thn one phse Solubility imit: Mximum concentrtion for which only single phse solution exists. Question: Wht is the solubility limit for sugr in wter t 20ºC? Answer: 65 wt% sugr. At 20ºC, if C < 65 wt% sugr: syrup At 20ºC, if 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) C = Composition (wt% sugr) Chpter 9-2

3 Components nd Phses Components: The elements or compounds which re present in the lloy (e.g., Al nd Cu) Phses: The physiclly nd chemiclly distinct mteril regions tht form (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

4 Temperture (ºC) Effect of Temperture & Composition Altering T cn chnge # of phses: pth A to B. Altering C cn chnge # of phses: pth B to D. wtersugr system Adpted from Fig. 9.1, Cllister & Rethwisch 8e ( liquid solution i.e., syrup) B (100ºC,C = 70) 1 phse (liquid) + S (solid sugr) C = Composition (wt% sugr) D (100ºC,C = 90) 2 phses A (20ºC,C = 70) 2 phses Chpter 9-4

5 Criteri for Solid Solubility Simple system (e.g., Ni-Cu solution) Crystl Structure electroneg r (nm) Ni FCC Cu FCC Both hve the sme crystl structure (FCC) nd hve similr electronegtivities nd tomic rdii (W. Hume Rothery rules) suggesting high mutul solubility. Ni nd Cu re totlly soluble in one nother for ll proportions. Chpter 9-5

6 Phse Digrms Indicte phses s function of T, C, nd P. For this course: - binry systems: just 2 components. - independent vribles: T nd C (P = 1 tm is lmost lwys used). Phse Digrm for Cu-Ni system (liquid) (FCC solid solution) phses: (liquid) (FCC solid solution) 3 different phse fields: + 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

7 Isomorphous Binry Phse Digrm Phse digrm: Cu-Ni system. System is: -- binry i.e., 2 components: Cu nd Ni. -- isomorphous i.e., complete solubility of one component in nother; phse field extends from 0 to 100 wt% Ni (liquid) (FCC solid solution) 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

8 Phse Digrms: Determintion of phse(s) present Rule 1: If we know T nd C o, then we know: -- which phse(s) is (re) present. 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) (liquid) B (1250ºC,35) (FCC solid solution) A(1100ºC,60) Cu-Ni phse digrm wt% Ni Chpter 9-8

9 Phse Digrms: Determintion of phse compositions Rule 2: If we know T nd C 0, then we cn determine: -- the composition of ech phse. Exmples: Consider C 0 = 35 wt% Ni At T A = 1320ºC: Only iquid () present C = C 0 ( = 35 wt% Ni) At T D = 1190ºC: Only Solid () present C = C 0 ( = 35 wt% Ni) At T B = 1250ºC: Both nd 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 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

10 Phse Digrms: Determintion of phse weight frctions Rule 3: If we know T nd C 0, then cn determine: -- the weight frction of ech phse. Exmples: Consider C 0 = 35 wt% Ni At T A : Only iquid () present At T D : At T B : W W W = 1.00, W = 0 Only Solid ( ) present W = 0, W = 1.00 Both nd present S R + S R R + S = 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 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

11 The ever Rule Tie line connects the phses in equilibrium with ech other lso sometimes clled n isotherm 1300 T B 1200 (liquid) R B tie line S (solid) Wht frction of ech phse? Think of the tie line s lever (teeter-totter) M M C 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

12 Ex: Cooling of Cu-Ni Alloy Phse digrm: Cu-Ni system. Consider microstucturl chnges tht ccompny the cooling of C 0 = 35 wt% Ni lloy 1300 : 35 wt% Ni : 46 wt% Ni (liquid) (solid) A B C 24 D 36 E : 35wt%Ni Cu-Ni system : 32 wt% Ni : 43 wt% Ni : 24 wt% Ni : 36 wt% Ni Adpted from Fig. 9.4, Cllister & Rethwisch 8e C 0 wt% Ni Chpter 9-12

13 Cored vs Equilibrium Structures C chnges s we solidify. Cu-Ni cse: First to solidify hs C = 46 wt% Ni. st to solidify hs C = 35 wt% Ni. Slow rte of cooling: Equilibrium structure Uniform C : 35 wt% Ni Fst rte of cooling: Cored structure First to solidify: 46 wt% Ni st to solidify: < 35 wt% Ni Chpter 9-13

14 Tensile Strength (MP) Elongtion (%E) Mechnicl Properties: Cu-Ni System Effect of solid solution strengthening on: -- Tensile strength (TS) -- Ductility (%E) TS for pure Cu Cu Ni Composition, wt% Ni Adpted from Fig. 9.6(), Cllister & Rethwisch 8e. TS for pure Ni %E for pure Cu Cu Ni %E for pure Ni Composition, wt% Ni Adpted from Fig. 9.6(b), Cllister & Rethwisch 8e. Chpter 9-14

15 Binry-Eutectic Systems 2 components Ex.: Cu-Ag system 3 single phse regions (,, b) imited solubility: : mostly Cu b: mostly Ag T E : No liquid below T E C E : Composition t temperture T E Eutectic rection (C E ) (C E ) + b(c be ) cooling hs specil composition with min. melting T. + (liquid) b Cu-Ag system Adpted from Fig. 9.7, Cllister & Rethwisch 8e. + b b T ºC E ( 71.9 wt% Ag) (8.0 wt% Ag) b(91.2 wt% Ag) heting C E C, wt% Ag Chpter 9-15

16 EX 1: Pb-Sn Eutectic System For 40 wt% Sn-60 wt% Pb lloy t 150ºC, determine: -- the phses present Pb-Sn Answer: + b system -- the phse compositions Answer: C = 11 wt% Sn C b = 99 wt% Sn -- the reltive mount of ech phse Answer: W = S C b - C = 0 R+S C b - C = W b = = R = R+S = 59 = C 0 - C C b - C = = ºC 18.3 R (liquid) + b + b C C 0 Adpted from Fig. 9.8, Cllister & Rethwisch 8e. S C, wt% Sn C b Chpter 9-16 b

17 EX 2: Pb-Sn Eutectic System For 40 wt% Sn-60 wt% Pb lloy t 220ºC, determine: -- the phses present: Pb-Sn Answer: + system -- the phse compositions Answer: C = 17 wt% Sn C = 46 wt% Sn -- the reltive mount of ech phse Answer: W = C - C 0 C - C = = 6 29 = 0.21 W = C 0 - C = 23 C - C = (liquid) 183ºC + b + b C 0 C R Adpted from Fig. 9.8, Cllister & Rethwisch 8e. S C C, wt% Sn Chpter 9-17 b

18 Microstructurl Developments in Eutectic Systems I For lloys for which C 0 < 2 wt% Sn Result: t room temperture -- polycrystlline with grins of phse hving composition C T E : C 0 wt% Sn : C 0 wt% Sn + (Pb-Sn System) b Adpted from Fig. 9.11, Cllister & Rethwisch 8e. 0 C (room T solubility limit) 30 C, wt% Sn Chpter 9-18

19 Microstructurl Developments in Eutectic Systems II For lloys for which 2 wt% Sn < C 0 < 18.3 wt% Sn Result: t tempertures in + b rnge -- polycrystlline with grins nd smll b-phse prticles T E b : C 0 wt% Sn : C 0 wt% Sn b Pb-Sn system Adpted from Fig. 9.12, Cllister & Rethwisch 8e C 0 (sol. limit t T room ) 18.3 (sol. limit t T E ) 30 C, wt% Sn Chpter 9-19

20 Microstructurl Developments in Eutectic Systems III For lloy of composition C 0 = C E Result: Eutectic microstructure (lmellr structure) -- lternting lyers (lmelle) of nd b phses. 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 C E C, wt% Sn Chpter 9-20

21 mellr Eutectic Structure Adpted from Figs & 9.15, Cllister & Rethwisch 8e. Chpter 9-21

22 Microstructurl Developments in Eutectic Systems IV For lloys for which 18.3 wt% Sn < C 0 < 61.9 wt% Sn Result: phse prticles nd eutectic microconstituent 300 Pb-Sn system 200 T E R R + b Adpted from Fig. 9.16, Cllister & Rethwisch 8e. : C 0 wt% Sn S S + b C, wt% Sn b primry eutectic eutectic b Just bove T E : C = 18.3 wt% Sn C = 61.9 wt% Sn S W = = 0.50 R + S W = (1- W ) = 0.50 Just below T E : C = 18.3 wt% Sn C b = 97.8 wt% Sn W S = = 0.73 R + S W b = 0.27 Chpter 9-22

23 Hypoeutectic & Hypereutectic Adpted from Fig. 9.8, Cllister & Rethwisch 8e. (Fig dpted from Binry Phse Digrms, 2nd ed., Vol. 3, T.B. Msslski (Editor-in-Chief), ASM Interntionl, Mterils Prk, OH, 1990.) (Figs nd 9.17 from Metls Hndbook, 9th ed., Vol. 9, Metllogrphy nd Microstructures, Americn Society for Metls, Mterils Prk, OH, 1985.) T E hypoeutectic: C 0 = 50 wt% Sn 175 m Adpted from Fig. 9.17, Cllister & Rethwisch 8e. + b + b 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

24 Intermetllic Compounds Adpted from Fig. 9.20, Cllister & Rethwisch 8e. Mg 2 Pb Note: intermetllic compound exists s line on the digrm - not n re - becuse of stoichiometry (i.e. composition of compound is fixed vlue). Chpter 9-24

25 Eutectic, Eutectoid, & Peritectic Eutectic - liquid trnsforms to two solid phses cool + b (For Pb-Sn, 183ºC, 61.9 wt% Sn) het Eutectoid one solid phse trnsforms to two other solid phses intermetllic compound - cementite S 2 S 1 +S 3 cool + Fe 3 C (For Fe-C, 727ºC, 0.76 wt% C) het Peritectic - liquid nd one solid phse trnsform to second solid phse S 1 + S 2 cool + (For Fe-C, 1493ºC, 0.16 wt% C) het Chpter 9-25

26 Eutectoid & Peritectic Cu-Zn Phse digrm Peritectic trnsformtion + Eutectoid trnsformtion + Adpted from Fig. 9.21, Cllister & Rethwisch 8e. Chpter 9-26

27 Fe 3 C (cementite) Iron-Crbon (Fe-C) Phse Digrm 2 importnt points - Eutectic (A): + Fe 3 C - Eutectoid (B): + Fe 3 C (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.) (Fe) 0.76 Adpted from Fig. 9.24, Cllister & Rethwisch 8e C, wt% C Fe 3 C (cementite-hrd) (ferrite-soft) Chpter 9-27

28 0.76 Fe 3 C (cementite) (ustenite) (Fe) perlite C 0 Hypoeutectoid Steel 727ºC 1148ºC + Fe 3 C + Fe 3 C +Fe 3 C C, wt% C (Fe-C System) Adpted from Figs nd 9.29,Cllister & Rethwisch 8e. (Fig dpted from Binry Alloy Phse Digrms, 2nd ed., Vol. 1, T.B. Msslski (Ed.-in- Chief), ASM Interntionl, Mterils Prk, OH, 1990.) 100 m Hypoeutectoid steel perlite Adpted from Fig. 9.30, Cllister & Rethwisch 8e. proeutectoid ferrite Chpter 9-28

29 0.76 Fe 3 C (cementite) W = s/(r + s) W =(1 - W ) W perlite = W W = S/(R + S) + (ustenite) r perlite (Fe) C 0 Hypoeutectoid Steel 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 nd 9.29,Cllister & Rethwisch 8e. (Fig 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

30 0.76 Fe 3 C (cementite) Fe 3 C Hypereutectoid Steel + (ustenite) (Fe) perlite C ºC +Fe 3 C +Fe 3 C +Fe 3 C C, wt%c (Fe-C System) Adpted from Figs nd 9.32,Cllister & Rethwisch 8e. (Fig 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

31 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) W =(1 - W ) Fe 3 C (ustenite) 600 perlite +Fe 3 C (Fe) Hypereutectoid Steel 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 nd 9.32,Cllister & Rethwisch 8e. (Fig 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

32 Exmple Problem For 99.6 wt% Fe-0.40 wt% C steel t temperture just below the eutectoid, determine the following: ) The compositions of Fe 3 C nd ferrite (). b) The mount of cementite (in grms) tht forms in 100 g of steel. c) The mounts of perlite nd proeutectoid ferrite () in the 100 g. Chpter 9-32

33 Fe C (cementite) W Fe 3 C R R S Solution to Exmple Problem ) Using the RS tie line just below the eutectoid C = wt% C C Fe3 C = 6.70 wt% C b) Using the lever rule with the tie line shown C 0 C C Fe 3 C C Amount of Fe 3 C in 100 g (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 C, wt% C C C 0 Chpter 9-33 C Fe C 3

34 Fe C (cementite) Solution to Exmple Problem (cont.) c) Using the VX tie line just bove the eutectoid nd relizing tht W perlite C 0 = 0.40 wt% C C = wt% C C perlite = C = 0.76 wt% C V V X C 0 C C C Amount of perlite in 100 g (ustenite) V X + 727ºC 1148ºC + Fe 3 C + Fe 3 C +Fe 3 C = (100 g)w perlite = (100 g)(0.512) = 51.2 g C C C, wt% C C 0 Chpter 9-34

35 VMSE: Interctive Phse Digrms Microstructure, phse compositions, nd phse frctions respond interctively Chnge lloy composition Chpter 9-35

36 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 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 from Edgr C. Bin, Functions of the Alloying Elements in Steel, Americn Society for Metls, 1939, p. 127.) Chpter 9-36

37 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