Phase Diagrams

Definition and Basic Concepts Solubility Limit

Homogenous system (Homo=) 2 Heterogenous system (Hetero=) (Phase) - 2 phase

Binary Phase Diagrams Phase diagram T, oC , P Binary Phase diagram 2 T oC P=1 atm

1 phase liquid

2 phase liquid() Solid()

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(Binary Isomorphous System) phase diagram Cu-Ni

Liquidus: Solidus: 1) A 1 : (solid) B 2 : L(liquid) + (solid) 2) A Ni 60 wt% Cu 40 wt% B L Tie line liquidus

LC (Ni ) =32 wt% solidus C (Ni ) = 43 wt% 3) A

LW = 0 wt%, W = 100 wt% B Lever rule (Liquid)

oL

L

C CSW 73 wt%R S C

.C

( ) o L

L

C CRW 27 wt%R S C

.C

LW W 100%

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9.12 A 50 wt% Ni50 wt% Cu alloy is slowly cooled from 1400 C to 1200 C . (a) At what temperature does the first solid phase form? (b) What is the composition of this solid phase? (c) At what temperature does the liquid solidify? (d) What is the composition of this last remaining liquid phase? 9.17 A 65 wt% Ni35 wt% Cu alloy is heated to a temperature within the + liquid-phase region. If the composition of the phase is 70 wt% Ni, determine: (a) The temperature of the alloy (b) The composition of the liquid phase (c) The mass fractions of both phases oC = 65 wt% Ni C =70 wt% Ni (a) C solidus line 1340 C (b) tie line liquidus line LC =59 wt% Ni (c) o L

L

C C 65 59W 0.55C C 70 59

LW 1 W 1 0.55 0.45

liquidus line T (a) 1320 C (b) tie line solidus line (Ni)C 62 t%.w

(Cu)C 100 62 38 wt%. solidus line (c) 1270 C (d) tie line liquidus line L(Ni)C 37 %.wt

L(Cu)C 100 37 63 wt%.

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Equilibrium structure

Ni Ni Ni solidus Ni Cored structure Cored structure Equilibrium structure Homogenization

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(Mechanical Properties of Isomorphous Alloys) (solid solution strengthening)

Binary Eutectic System Binary isomorphous syatem: Binary eutectic system: ( , )

NOTE: Tensile strength (%EL)

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Cu-Ag 3 phase L, Cu Ag () E Invariant point EC 71.9 g.wt%A () ET 779 C () cooling

heatingL(71.9 wt% Ag) (8.0 wt% Ag) (91.2 w. . . . . t% Ag. )

ET Eutectic isotherm phase Solvus line Microstructures in Eutectic System phase diagram Pb-Sn 4

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1) 1C : L [ L L ] [ ] ( )

2) 2C : L L solvus line Sn

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3) : L eutectic Eutectic microstructure

4) : phase L Primary Eutectic isotherm L Eutectic eutectic Hypoeutectic eutectic Hypereutectic

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9.32 For a leadtin alloy of composition 80 wt% Sn20 wt% Pb and at 180 C ( 355 F ) do the following: (a) Determine the mass fractions of and phases. (b) Determine the mass fractions of primary and eutectic microconstituents. (c) Determine the mass fraction of eutectic

(a) oC C 98 80W 0.22C C 98 17

W 1.00 W 1.00 0.22 0.78 (b) primary eutectic microconstituents ( eutectic + ) eutectic isotherm (phase L ) primary

80 61.9W 0.597.8 61.9

eutectic primaryW 1.00 W 0.5 (c) eutectic primaryW W W 0.78 0.5 0.28

C oC C

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9.33 The microstructure of a coppersilver alloy at 775 C (1425 F ) consists of primary and eutectic structures. If the mass fractions of these two microconstituents are 0.73 and 0.27, respectively, determine the composition of the alloy. primary eutectic isotherm

L oprimary

L

C CWC C

o71.9 C0.73

71.9 8.0

oC 25.25 wt% Ag

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Invariant Reactions Invariant point V Eutectic coolingL Eutectoid cooling Peritectic coolingL Peritectoid cooling : Eu- 1 phase 2 phase V Peri- 2 phase 1 phase -tic phase (L) -toid phase (L)

Congruent Phase Tranformation Congruent Incongruent 1 Congruent phase diagram L

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The Iron Carbon System

phase (Ferrite Fe) - iron BCC (Austenite) - iron FCC - iron BCC (Cementite) 3Fe C Carbon 6.67% (Pearlite) Ferrite + Cementite 2

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Microstructure in Iron-Carbon Alloys austenite pearlite (ferrite + cementite)

Hypoeutectoid steel

2 ferrite ( ) cementite ( 3Fe C) 2 8:1 pearlite pearlite C C ferrite( ) cementite( 3Fe C)

d austenite( ) ferrite( ) Proeutectoid ferrite Eutectoid temperature austenite( ) pearlite pearlite Eutectoid ferrite

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Hypereutectoid steel

Alloying Steel pearlite

cementite( 3Fe C) Eutectiod temperature Proeutectoid cementite Proeutectoid ferrite Eutectoid temperature austenite( ) pearlite 3Fe C pearlite Eutectoid cementite

C

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9.42 Figure 9.36 is the tingold phase diagram, for which only single-phase regions are labeled. Specify temperaturecomposition points at which all eutectics, eutectoids, peritectics, and congruent phase transformations occur. Also, for each, write the reaction upon cooling.

Eutectic: 1 Liquid 2 Solids (1) 10 wt% Au, 217 C L (2) 80 wt% Au, 280 C L Eutectoid: 1 Solid 2 Solids -None- Peritectic: 1 Liquid + 1 Solid 1 Solid (1) 30 wt% Au, 252 C L (2) 45 wt% Au, 309 C L (3) 92 wt% Au, 490 C L Congruent phase transformation: 1 phase 1 phase (1) 62.5 wt% Au, 418 C L

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9.58 Is it possible to have an ironcarbon alloy for which the mass fractions of total cementite and proeutectoid ferrite are 0.057 and 0.36, respectively? Why or why not? W proeutectoid ferrite = 0.36 oC

oproeutectoid

C CW

C C

o0.76 C0.360.76 0.022

oC 0.49 wt% C W cementite = 0.057 oC =0.49 wt% C C

3

3

oFe C

Fe C

C CWC C

0.49 C0.0576.7 C

C 0.11 wt% C ferrite 0.022 wt% C

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