Phase Equilibria: Solubility Limit PHASE DIAGRAMS 10 0 Solubility 8 0 Limit ENT 145 Materials Engineering (liquid) atu (liquid solution 4 0

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1 Temperture (ºC) ter ugr Temperture (ºC) Phse Equilibri: olubility imit PHE DIGM ENT 145 Mterils Engineering Chpter 9 - olution solid, liquid, or gs solutions, single phse Mixture more thn one phse olubility imit: Mximum concentrtion of solute tom tht my dissolve in solvent to form solid solution. Question: ht is the solubility limit for sugr in wter t ºC? 1 nswer: 65 wt% sugr. t ºC, if C < 65 wt% sugr: syrup t ºC, if C > 65 wt% sugr: syrup + sugr ugr/ter Phse Digrm olubility imit (liquid solution i.e., syrup) dpted from Fig. 9.1, Cllister & ethwisch 8e. (liquid) + (solid sugr) C = Composition (wt% sugr) Chpter 9-2 Components: The elements or compounds which re present in the lloy (e.g., l nd Cu) Phses: Homogeneous portion of tht hs uniform physicl nd chemicl chrcteristics (e.g., nd b). luminum- Copper lloy dpted from chpteropening photogrph, Chpter 9, Cllister, Mterils cience & Engineering: n Introduction, 3e. Components nd Phses b (lighter phse) (drker phse) Chpter 9-3 Effect of Temperture & Composition ltering T cn chnge # of phses: pth to. ltering C cn chnge # of phses: pth to D. (1ºC,C = 7) D (1ºC,C = 9) 1 phse 2 phses 1 wtersugr dpted from Fig. 9.1, Cllister & ethwisch 8e ( liquid solution i.e., syrup) (liquid) + (solid sugr) (ºC,C = 7) 2 phses C = Composition (wt% sugr) Chpter 9-4 Criteri for olid olubility imple (e.g., -Cu Crystl tructure electroneg r (nm) FCC Cu FCC oth hve the sme crystl structure (FCC) nd hve similr electronegtivities nd tomic rdii (. Hume othery rules) suggesting high mutul solubility. nd Cu re totlly soluble in one nother for ll proportions. Chpter 9-5 Phse Digrms Indicte phses s function of T, C, nd P. For this course: - binry s: just 2 components. - independent vribles: T nd C (P = 1 tm is lmost lwys used). Phse Digrm for (liquid) wt% 2 phses: (liquid) 3 different phse fields: + dpted from Fig. 9.3(), Cllister & ethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of inry ckel lloys, P. Nsh (Ed.), M Interntionl, Mterils Prk, OH (1991). Chpter 9-6 1

2 Isomorphous inry Phse Digrm Phse digrm:. ystem is: -- binry i.e., 2 components: Cu nd. -- isomorphous i.e., complete solubility of one component in nother; phse field extends from to 1 wt% (liquid) dpted from Fig. 9.3(), Cllister & ethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of inry ckel lloys, P. Nsh (Ed.), M Interntionl, Mterils Prk, OH (1991). phse digrm wt% Chpter 9-7 Phse Digrms: Determintion of phse(s) present ule 1: If we know T nd C o, then we know: -- which phse(s) is (re) present. Exmples: (11ºC, 6 wt% ): 1 phse: (125ºC, 35 wt% ): 2 phses: + dpted from Fig. 9.3(), Cllister & ethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of inry ckel lloys, P. Nsh (Ed.), M Interntionl, Mterils Prk, OH (1991) (liquid) (125ºC,35) (11ºC,6) phse digrm wt% Chpter 9-8 Phse Digrms: Determintion of phse compositions ule 2: If we know T nd C, then we cn determine: -- the composition of ech phse. Exmples: Consider C = 35 wt% t T = 13ºC: Only iquid () present C = C ( = 35 wt% ) t T D = 119ºC: Only olid () present C = C ( = 35 wt% ) t T = 125ºC: oth nd present C = C liquidus ( = 32 wt% ) C = C solidus ( = 43 wt% ) T 13 (liquid) T T D D C C C wt% dpted from Fig. 9.3(), Cllister & ethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of inry ckel lloys, P. Nsh (Ed.), M Interntionl, Mterils Prk, OH (1991). Chpter 9-9 Phse Digrms: Determintion of phse weight frctions ule 3: If we know T nd C, then cn determine: -- the weight frction of ech phse. Exmples: Consider C = 35 wt% T t T : Only iquid () present 13 (liquid) = 1., = t T D : Only olid ( ) present T =, = 1. D t T : oth nd present T D = C C C wt% dpted from Fig. 9.3(), Cllister & ethwisch 8e. (Fig. 9.3() is dpted from Phse Digrms of inry ckel lloys, P. Nsh (Ed.), M Interntionl, Mterils Prk, OH (1991). Chpter 9-1 The ever ule Tie line connects the phses in equilibrium with ech other lso sometimes clled n isotherm 13 T (liquid) 3 C 4 5 C C wt% M C C M M C C dpted from Fig. 9.3(b), Cllister & ethwisch 8e. ht frction of ech phse? Think of the s lever (teeter-totter) M M M x M x C C C C Chpter 9-11 Ex: Cooling of lloy Phse digrm:. Consider microstucturl chnges tht ccompny the ing of C = 35 wt% lloy (liquid) 13 : 35 wt% : 46 wt% 1 11 dpted from Fig. 9.4, Cllister & ethwisch 8e C 24 D 36 E : 35wt% C wt% Chpter 9-12 : 32 wt% : 43 wt% : 24 wt% : 36 wt% 2

3 .76 Tensile trength (MP) Elongtion (%E) Cored vs Equilibrium tructures C chnges s we solidify. cse: First to solidify hs C = 46 wt%. st to solidify hs C = 35 wt%. low rte of ing: Equilibrium structure Uniform C : 35 wt% Fst rte of ing: Cored structure First to solidify: 46 wt% st to solidify: < 35 wt% Mechnicl Properties: ystem Effect of solid solution strengthening on: -- Tensile strength (T) -- Ductility (%E) 4 3 T for pure Cu Cu Composition, wt% dpted from Fig. 9.6(), Cllister & ethwisch 8e. T for pure %E for pure Cu %E for pure Cu Composition, wt% dpted from Fig. 9.6(b), Cllister & ethwisch 8e. Chpter 9-13 Chpter 9-14 Eutectic, Eutectoid, & Peritectic Eutectic - liquid trnsforms to two solid phses + b (For Pb-n, 183ºC, 61.9 wt% n) het Eutectoid one solid phse trnsforms to two other solid phses intermetllic compound cementite 3 + Fe 3 C (For Fe-C,,.76 wt% C) het Peritectic - liquid nd one solid phse trnsform to second solid phse Eutectoid & Peritectic Cu-Zn Phse digrm Peritectic trnsformtion (For Fe-C, 1493ºC,.16 wt% C) het Eutectoid trnsformtion + dpted from Fig. 9.21, Cllister & ethwisch 8e. Chpter 9-15 Chpter 9-16 Iron-Crbon ) Phse Digrm 2 importnt points - Eutectic (): + Fe 3 C - Eutectoid (): + Fe 3 C 1 mm esult: Perlite = lternting lyers of nd Fe 3 C phses (dpted from Fig. 9.27, Cllister & ethwisch 8e.) + (ustenite) (Fe) C, wt% C dpted from Fig. 9.24, Cllister & ethwisch 8e. +Fe 3 C = T eutectoid +Fe 3 C +Fe 3 C Fe 3 C (cementite-hrd) (ferrite-soft) Chpter (ustenite) + Fe 3 C Hypoeutectoid teel + Fe 3 C +Fe 3 C (Fe) C C, wt% C perlite perlite dpted from Fig. 9.3, Cllister & ethwisch 8e. ystem) 1 mm Hypoeutectoid dpted from Figs nd 9.29,Cllister & ethwisch 8e. (Fig dpted from inry lloy Phse Digrms, 2nd ed., Vol. 1, T.. Msslski (Ed.-in- Chief), M Interntionl, Mterils Prk, OH, 199.) proeutectoid ferrite Chpter

4 Hypoeutectoid teel + (ustenite) +Fe 3 C = s/(r + s) + Fe 3 C r s =(1 - ) + Fe 3 C perlite perlite = (Fe) C C, wt% C = /( + ) Fe 3C =(1 ) perlite dpted from Fig. 9.3, Cllister & ethwisch 8e. ystem) 1 mm Hypoeutectoid dpted from Figs nd 9.29,Cllister & ethwisch 8e. (Fig dpted from inry lloy Phse Digrms, 2nd ed., Vol. 1, T.. Msslski (Ed.-in- Chief), M Interntionl, Mterils Prk, OH, 199.) proeutectoid ferrite Chpter 9-19 Fe 3C Hypereutectoid teel + (ustenite) +Fe 3 C +Fe 3 C +Fe 3 C 4 1 C (Fe) C, wt%c perlite perlite dpted from Fig. 9.33, Cllister & ethwisch 8e. ystem) 6 mm Hypereutectoid proeutectoid Fe 3 C dpted from Figs nd 9.32,Cllister & ethwisch 8e. (Fig dpted from inry lloy Phse Digrms, 2nd ed., Vol. 1, T.. Msslski (Ed.-in-Chief), M Interntionl, Mterils Prk, OH, 199.) Chpter 9 - Hypereutectoid teel Fe 3C + ystem) +Fe (ustenite) 3 C +Fe 3 C =x/(v + x) v x Fe 3C =(1- ) V X +Fe 3 C perlite dpted from Figs nd 9.32,Cllister & ethwisch 8e. (Fig dpted from inry lloy Phse Digrms, 2nd ed., Vol. 1, T.. Msslski (Ed.-in-Chief), M Interntionl, Mterils Prk, OH, 199.) 4 1 C perlite = (Fe) C, wt%c Exercise For 99.6 wt% Fe-.4 wt% C t temperture just below the eutectoid, determine the following: ) The compositions of Fe 3 C nd ferrite (). b) The mounts of perlite nd proeutectoid ferrite () in the 1 g. c) The mount of cementite (in grms) tht forms in 1 g of. = X/(V + X) =(1 - ) Fe 3C perlite 6 mm Hypereutectoid proeutectoid Fe 3 C dpted from Fig. 9.33, Cllister & ethwisch 8e. Chpter 9-21 Chpter 9-22 olution to Exercise Problem ) Using the just below the eutectoid Using the lever rule with the shown Fe 3 C C C C Fe 3 C C C =.22 wt% C C Fe3C = 6.7 wt% C mount of Fe 3 C in 1 g = (1 g) Fe3C = (1 g)(.57) = 5.7 g + (ustenite) + Fe 3 C + Fe 3 C +Fe 3 C C C C, wt% C C Fe 3 C Chpter 9-23 olution to Exercise Problem (cont.) b) Using the VX just bove the eutectoid nd relizing tht C =.4 wt% C C =.22 wt% C C perlite = C =.76 wt% C V perlite V X C C C C mount of perlite in 1 g = (1 g) perlite + (ustenite) = (1 g)(.512) = 51.2 g V X + Fe 3 C + Fe 3 C +Fe 3 C C C C C, wt% C Chpter

5 T Eutectoid (ºC) C eutectoid (wt% C) lloying with Other Elements T eutectoid chnges: C eutectoid chnges: Ti Mo i Cr Mn Cr i Ti Mo Mn wt. % of lloying elements dpted from Fig. 9.34,Cllister & ethwisch 8e. (Fig from Edgr C. in, Functions of the lloying Elements in teel, mericn ociety for Metls, 1939, p. 127.) wt. % of lloying elements dpted from Fig. 9.35,Cllister & ethwisch 8e. (Fig from Edgr C. in, Functions of the lloying Elements in teel, mericn ociety for Metls, 1939, p. 127.) Chpter