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(1)

ISSUES TO ADDRESS...

• When we combine two elements...

what is the resulting equilibrium state?

• In particular, if we specify...

-- the composition (e.g., wt% Cu - wt% Ni), and -- the temperature (T )

then...

How many phases form?

What is the composition of each phase?

What is the amount of each phase?

Chapter 9: 상태도(Phase Diagrams)

Phase B Phase A

Nickel atom

Copper atom

(2)

Chapter 9 - 2

상평형(Phase Equilibria):

용해 한도(Solubility Limit)

Question: 20ºC 에서 물에 대한 설탕의 용해 한도는?

Answer: 65 wt% sugar .

20ºC, C < 65 wt% sugar: syrup

20ºC, C > 65 wt% sugar: syrup + sugar

65

• 용해 한도(Solubility Limit):

단상으로 구성하는 용매에 용해되는 용질의 최대 농도

Sugar/Water Phase Diagram

Sugar

T em pera ture (º C)

0 20 40 60 80 100

C = Composition (wt% sugar)

L

(liquid solution i.e., syrup)

Solubility

Limit L

(liquid)

+ S

(solid sugar) 20

4 0 6 0 8 0 10 0

W ater

Adapted from Fig. 9.1, Callister & Rethwisch 8e.

고용체

– 고체, 액체, 기체상의 단상으로 구성

혼합

– 한 상 이상으로 구성

(3)

• 성분(components):

합금을 구성하는 순금속이나 화합물 (e.g., Al and Cu)

• 상(phases):

물리적·화학적 특성이 균일한 계의 균질한 부분 (e.g., a and b).

Aluminum- Copper Alloy

성분과 상(Components and Phases)

a (darker phase)

b (lighter phase)

Adapted from chapter- opening photograph, Chapter 9, Callister, Materials Science &

Engineering: An Introduction, 3e.

(4)

Chapter 9 - 4

70 80 100 60

40 20

0

T empera ture (º C)

C = Composition (wt% sugar)

L

( liquid solution i.e., syrup)

20 100

40 60 80

0

L

(liquid)

+ S

(solid sugar)

온도와 조성의 영향

• 온도(T)의 변화 – 상의 변화: path A to B.

• 조성(C)의 변화 – 상의 변화: path B to D.

water- sugar system

Adapted from Fig. 9.1, Callister & Rethwisch 8e.

D (100ºC,C = 90)

2 phases

B (100ºC,C = 70)

1 phase

A (20ºC,C = 70)

2 phases

(5)

고용체의 기준(Criteria for Solid Solubility)

Crystal Structure

electroneg r (nm)

Ni FCC 1.9 0.1246

Cu FCC 1.8 0.1278

• 두 가지 모두 같은 결정구조(FCC), 유사한 전기 음성도와 원자 반경(W. Hume – Rothery rules)는 높은 상호 고용도를 예측할 수 있음

단순 계 (e.g., Ni-Cu solution)

• Ni와 Cu는 모든 조성에서 서로 완전한 용해도를 보임

(6)

Chapter 9 - 6

상태도(Phase Diagrams)

• T, C와 P에 따른 상(phase) 구분

• 본 강의에서:

- 2원계(binary systems): 2가지 성분으로 구성 - 독립 변수: 온도(T)와 성분(C) (P = 1 atm, 대기압)

Phase Diagram for Cu-Ni system

Adapted from Fig. 9.3(a), Callister &

Rethwisch 8e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International,

Materials Park, OH (1991).

• 2 phases:

L (liquid)

a (FCC solid solution)

• 3가지 다른 상 영역:

L

L + a a

wt% Ni

20 40 60 80 100 1000 0

1100 1200 1300 1400 1500 1600

T(ºC)

L (liquid)

a

(FCC solid solution)

(7)

Cu-Ni phase diagram

전율고용 2원계 상태도

(Isomorphous Binary Phase Diagram)

• Phase diagram:

Cu-Ni system.

• System is:

Adapted from Fig. 9.3(a), Callister &

Rethwisch 8e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International,

Materials Park, OH (1991).

-- 2원계(binary) i.e., 2가지 조성:

Cu와 Ni

-- 전율고용체(isomorphous) i.e., 두 성분이 액상과

고상에서 서로 완전한 용해도를 갖음; a phase field extends from

0 to 100 wt% Ni.

wt% Ni

20 40 60 80 100 1000 0

1100 1200 1300 1400 1500 1600

T(ºC)

L (liquid)

a

(FCC solid solution)

(8)

Chapter 9 -

wt% Ni

20 40 60 80 100 1000 0

1100 1200 1300 1400 1500 1600

T(ºC)

L (liquid)

a

(FCC solid

solution)

Cu-Ni phase diagram

8

Phase Diagrams

:

상의 종류 결정

• Rule 1: T 와 C o 를 알면:

-- 존재하는 상(phase(s))의 종류를 알 수 있다.

• Examples:

A(1100ºC, 60 wt% Ni):

1 phase: a

B (1250ºC, 35 wt% Ni):

2 phases: L + a

B (12 50 ºC,35 )

A(1100ºC,60)

Adapted from Fig. 9.3(a), Callister &

Rethwisch 8e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International,

Materials Park, OH (1991).

(9)

wt% Ni

20 1200 1300

T(ºC)

L (liquid)

a (solid)

30 40 50

Cu-Ni system

Phase Diagrams

:

상의 조성 결정

• Rule 2: T 와 C o 를 알면 :

--개개 상의 조성을 알 수 있다.

• Examples:

T A A

35 C 0 32 C

L

T A = 1320ºC:

액상(L) 만이 존재

C L = C

0

( = 35 wt% Ni)

T B = 1250ºC:

두상 a 와 L 이 존재

C L = C liquidus ( = 32 wt% Ni) C a = C solidus ( = 43 wt% Ni) T D = 1190ºC:

고상(a) 만이 존재

C a = C

0

( = 35 wt% Ni) C 0 = 35 wt% Ni의 조성

T D D

tie line

4 C 3 a

Adapted from Fig. 9.3(a), Callister &

Rethwisch 8e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P.

Nash (Ed.), ASM International, Materials Park, OH (1991).

T B B

(10)

Chapter 9 - 10

• Rule 3: T 와 C o 를 알면 :

-- 개개 상의 무게 분율를 알 수 있다.

• Examples:

T A : 액상(L) 만이 존재

W L = 1.00, W a = 0 T D : 고상( a ) 만이 존재

W L = 0, W a = 1.00

Phase Diagrams :

상의 무게 분율(양) 결정

wt% Ni

20 1200 1300

T(ºC)

L (liquid)

a (solid)

3 0 4 0 5 0

Cu-Ni system

T A A

35 C 0 32 C L T B B

T D D

tie line

4 C 3 a

R S

T B : 두가지 a 와 L 존재

73 . 32 0

43

35

43 

 

= 0.27

W LS R + S

W aR R + S

C 0 = 35 wt% Ni

Adapted from Fig. 9.3(a), Callister &

Rethwisch 8e. (Fig. 9.3(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P.

Nash (Ed.), ASM International, Materials Park, OH (1991).

(11)

• 공액선(Tie line) – 평형상태에서 2상 구역 내 각 상의 경계선과 연결 – 등온선(isotherm)

지렛대 원리(The Lever Rule)

각 상의 분율은?

공액선(tie line)을 지렛대로 간주(lever) (teeter-totter 혹은 see-saw)

M

a

M

L

R S

M

a

x SM

L

x R

L L L

L L

L

C C

C C

S R

W R C

C

C C

S R

S M

M W M

 

 

 

 

 

a a

a a a

0 0

wt% Ni

20 1200 1300

T(ºC)

L (liquid)

a (solid)

3 0 4 0 5 0

T B B

tie line

C 0

C L

C a S

R

Adapted from Fig. 9.3(b), Callister & Rethwisch 8e.

(12)

Chapter 9 - 12

wt% Ni

20 120 0 130 0

3 0 4 0 5 0

110 0

L (liquid)

a (solid) T(ºC)

A

35 C 0

L: 35wt%Ni

Cu-Ni system

• 상태도:

Cu-Ni system.

Adapted from Fig. 9.4, Callister & Rethwisch 8e.

C 0 = 35 wt% Ni alloy의 냉각에

따르는 미세조직의 변화

Ex: Cu-Ni Alloy의 냉각

35 46 32 43

a: 43 wt% Ni L: 32 wt% Ni a: 46 wt% Ni L: 35 wt% Ni B

C

E L: 24 wt% Ni

a: 36 wt% Ni

24 D 36

(13)

• 느린 냉각속도:

평형 조직

• 빠른 냉각 속도:

유핵 조직

First a to solidify:

46 wt% Ni

Last a to solidify:

< 35 wt% Ni

• 냉각에 따른 C a 의 조성 변화

• Cu-Ni의 경우: 최초 고상 a 의 조성 C a = 46 wt% Ni.

최종 고상 a 의 조성 C a = 35 wt% Ni.

유핵 vs 평형 조직

(Cored vs Equilibrium Structures)

Uniform C a :

35 wt% Ni

(14)

Chapter 9 - 14

기계적 성질:

Cu-Ni System

• 고용체 강화의 영향:

-- Tensile strength (TS) -- Ductility (%EL)

Adapted from Fig. 9.6(a), Callister & Rethwisch 8e.

T en s ile Stre ng th (MPa)

Composition, wt% Ni

Cu Ni

0 20 40 60 80 100 200

300 400

TS for pure Ni

TS for pure Cu

Elon ga tion ( % EL )

Composition, wt% Ni

Cu 0 20 40 60 80 100 Ni 20

30 40 50 60

%EL for pure Ni

%EL for pure Cu

Adapted from Fig. 9.6(b), Callister & Rethwisch 8e.

(15)

2가지 조성

최소의 용해온도(T)를 갖는 특정 조성

Adapted from Fig. 9.7, Callister & Rethwisch 8e.

2원 공정계

(Binary-Eutectic Systems)

• 3개의 단일상 구역 (L, a, b)

• 제한된 용해도:

a: 대부분 Cu b: 대부분 Ag

• T E : T E 이하 액상 무 : 온도 T E 에서의 조성

• C E

Ex.: Cu-Ag system

Cu-Ag system

L (liquid) a L + a

L + b b

a  b

C , wt% Ag

20 40 60 80 100

200 0 1200

T(ºC)

400 600 800 1000

C

E

T E 8.0 71.9 91.2

779ºC

Ag) wt%

1.2 9 ( Ag)

wt%

.0 8 ( Ag)

wt%

9 . 71

( a  b

L cooling

• 공정 반응( Eutectic reaction)

L(C E ) a(C aE ) + b(C bE )

(16)

Chapter 9 - 16

L + a

L + b

a + b

200

T(ºC)

18.3

C, wt% Sn

20 60 80 100

0 300

100

L (liquid)

a 183ºC

61.9 97.8

b

• 150ºC 에서 40 wt% Sn-60 wt% Pb alloy:

-- 존재하는 상 Pb-Sn

system

EX 1: Pb-Sn 공정계

Answer: a + b -- 상의 조성

-- 각 상의 분율

150

40 C 0 11

C a 99

C b

R S

Answer: C a = 11 wt% Sn C b = 99 wt% Sn

W a = C

b

- C

0

C

b

- C

a

= 99 - 40

99 - 11 = 59

88 = 0.67 S

R+S =

W b = C

0

- C

a

C

b

- C

a

R =

R+S

= 29

88 = 0.33

= 40 - 11 99 - 11 Answer:

Adapted from Fig. 9.8, Callister & Rethwisch 8e.

(17)

Answer: C a = 17 wt% Sn -- 상조성

L + b

a + b

200

T(ºC)

C, wt% Sn

20 60 80 100

0 300

100

L (liquid)

a b

L + a

183ºC

• 220ºC에서 40 wt% Sn-60 wt% Pb alloy:

-- 존재 상: Pb-Sn

system

EX 2: Pb-Sn 공정계

-- 각 상의 분율

W a = C

L

- C

0

C

L

- C

a

= 46 - 40 46 - 17

= 6

29 = 0.21

W L = C

0

- C

a

C - C a = 23

29 = 0.79

40 C 0

46 C L 17

C a

220 R S

Answer: a + L

C L = 46 wt% Sn

Answer:

Adapted from Fig. 9.8, Callister & Rethwisch 8e.

(18)

Chapter 9 - 18

• C 0 < 2 wt% Sn의 합금

• 결과: 상온

-- C

0

의 조성을 갖는 a phase 결정으로 구성된 다결정

공정계의 미세조직 I

0

L + a

200

T(ºC)

C , wt% Sn

10 2

20 C

0

300

100

L a

30

a + b

400

(room T solubility limit)

T

E

(Pb-Sn

System)

a L L: C

0

wt% Sn

a: C

0

wt% Sn

Adapted from Fig. 9.11, Callister & Rethwisch 8e.

(19)

• 2 wt% Sn < C 0 < 18.3 wt% Sn 합금

• 결과:

a + b 구역 내의 온도

-- a grains과 작은 b-phase 입자를 갖는 다결정

Adapted from Fig. 9.12, Callister & Rethwisch 8e.

공정계의 미세조직 II

Pb-Sn system L + a

200

T(ºC)

C , wt% Sn

10

18.3 20 0

C

0

300

100

L

a

30

a + b

400

(sol. limit at T

E

) T

E

2

(sol. limit at T room )

L a L: C

0

wt% Sn

a b

a: C

0

wt% Sn

(20)

Chapter 9 - 20

• 합금의 조성: C 0 = C E

• 결과: 공정합금 미세조직, 층상 구조(lamellar structure) -- a와 b 상의 층상(lamellae) 구조

Adapted from Fig. 9.13, Callister & Rethwisch 8e.

공정합금의 미세조직 III

Adapted from Fig. 9.14, Callister & Rethwisch 8e.

160 m

Micrograph of Pb-Sn eutectic

microstructure

Pb-Sn system

L  b

a  b

200

T(ºC)

C, wt% Sn

20 60 80 100

0

300

100

L

a b

L + a

183ºC

40 T

E

18.3

a: 18.3 wt%Sn

97.8 b: 97.8 wt% Sn

C

E

61.9

L: C

0

wt% Sn

(21)

Lamellar Eutectic Structure

Adapted from Figs. 9.14 & 9.15, Callister

& Rethwisch 8e.

(22)

Chapter 9 - 22

• 18.3 wt% Sn < C 0 < 61.9 wt% Sn

• 결과: a상 입자와 공정형 미세구성인자

공정계의 미세조직 IV

18.3 61.9

S R

97.8 R S

primary a eutectic a

eutectic b

W

L

= (1- W a ) = 0.50 C a = 18.3 wt% Sn C

L

= 61.9 wt% Sn

S R + S

W a = = 0.50

• T E 직상 :

• T E 직하:

C a = 18.3 wt% Sn C b = 97.8 wt% Sn

S R + S

W a = = 0.73 W b = 0.27

Adapted from Fig. 9.16, Callister & Rethwisch 8e.

Pb-Sn system

L + b

200

T(ºC)

C, wt% Sn

20 60 80 100

0

300

100

L

a b

L + a

40

a + b

T

E

L: C 0 wt% Sn a L L

a

(23)

L + a

L + b a + b

200

C, wt% Sn

20 60 80 100

0 300

100

L

a b

TE

40

(Pb-Sn System)

아공석

(Hypoeutectic) &

공석

(Hypereutectic)

Adapted from Fig. 9.8, Callister & Rethwisch 8e.

(Fig. 10.8 adapted from Binary Phase Diagrams, 2nd ed., Vol. 3, T.B.

Massalski (Editor-in-Chief), ASM International,

Materials Park, OH, 1990.)

160 m eutectic micro-constituent

Adapted from Fig. 9.14,

hypereutectic: (illustration only)

b b b

b b

b

Adapted from Fig. 9.17, Callister & Rethwisch 8e.

(Figs. 9.14 and 9.17 from Metals

Handbook, 9th ed., Vol. 9,

Metallography and Microstructures, American Society for Metals, Materials Park, OH, 1985.)

175 m

a a

a a a

a

hypoeutectic: C0 = 50 wt% Sn

Adapted from Fig. 9.17, Callister &

T(ºC)

61.9 eutectic

eutectic: C0=61.9wt% Sn

(24)

Chapter 9 - 24

금속간 화합물(Intermetallic Compounds)

Mg 2 Pb

Note: 금속간 화합물은 상태도에 선으로 표시- 면적이 아님 – 정해진 화학식을 갖음 (i.e. 화합물의 조성이 정해짐).

Adapted from Fig. 9.20, Callister &

Rethwisch 8e.

(25)

• Eutectoid – 1개의 고상이 2개의 다른 고상으로 상변화

S 2 S 1 +S 3

 a + Fe 3 C (Fe-C의 경우, 727ºC, 0.76 wt%

C)

금속간 화합물 - cementite

cool heat

공정(Eutectic), 공석(Eutectoid), &

포정(Peritectic)

• Eutectic – 액상이 2개의 고상으로 상변화

L a + b (Pb-Sn의 경우, 183ºC, 61.9 wt% Sn) cool

heat

cool heat

• Peritectic – 액상과 고상이 다른 1개의 고상으로 상변화

S 1 + L S 2

 + L  (Fe-C의 경우, 1493ºC, 0.16 wt% C)

(26)

Chapter 9 - 26

Eutectoid & Peritectic

Cu-Zn Phase diagram

Adapted from Fig. 9.21, Callister & Rethwisch 8e.

Eutectoid transformation   + 

Peritectic transformation  + L 

(27)

Chapter 9 - 27

철-탄소 (Fe-C) 상태도

• 2 중요한 points

- Eutectoid (B):

  a + Fe

3

C

- Eutectic (A):

L   + Fe

3

C

Adapted from Fig. 9.24, Callister & Rethwisch 8e.

Fe

3

C (c ementit e)

1600 1400 1200

1000 800

600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

+Fe

3

C

a +Fe

3

C

(Fe) C, wt% C

1148ºC

T(ºC)

a 727ºC = T eutectoid

4.30

Result: Pearlite = alternating layers of a and Fe

3

C phases

120 m

(Adapted from Fig. 9.27, Callister & Rethwisch 8e.)

0.76

B

   

A L+Fe

3

C

Fe

3

C (cementite-hard)

a (ferrite-soft)

(28)

Chapter 9 - 28

Fe

3

C (c emen tit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

+ Fe

3

C

a + Fe

3

C

L+Fe

3

C

(Fe) C, wt% C

1148ºC

T(ºC)

a 727ºC

(Fe-C System)

C0

0.76

아공석

강(Hypoeutectoid Steel)

Adapted from Figs. 9.24 and 9.29,Callister &

Rethwisch 8e.

(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. 9.30, Callister & Rethwisch 8e.

proeutectoid ferrite pearlite

100 m Hypoeutectoid steel a

pearlite

 

a 

a a

   

   

(29)

Fe

3

C (c emen tit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

+ Fe

3

C

a + Fe

3

C

L+Fe

3

C

(Fe) C, wt% C

1148ºC

T(ºC)

a 727ºC

(Fe-C System)

C0

0.76

아공석

강(Hypoeutectoid Steel)

 

a 

a a

s r

W a = s/(r + s) W =(1 - W a )

R S

a

pearlite

W

pearlite

= W W a’ = S/(R + S) W Fe =(1 – W a’ )

3

C

Adapted from Figs. 9.24 and 9.29,Callister &

Rethwisch 8e.

(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 pearlite

100 m Hypoeutectoid

steel

(30)

Chapter 9 - 30

공석 강(Hypereutectoid Steel)

Fe

3

C (c emen tit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

+Fe

3

C

a +Fe

3

C

L+Fe

3

C

(Fe) C, wt%C

1148ºC

T(ºC)

a

Adapted from Figs. 9.24 and 9.32,Callister &

Rethwisch 8e. (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.)

(Fe-C System)

0 .7 6 C

0

Fe

3

C

 

 

   

   

Adapted from Fig. 9.33, Callister & Rethwisch 8e.

proeutectoid Fe

3

C

60 m Hypereutectoid steel

pearlite

pearlite

(31)

Fe

3

C (c emen tit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

+Fe

3

C

a +Fe

3

C

L+Fe

3

C

(Fe) C, wt%C

1148ºC

T(ºC)

a

공석 강(Hypereutectoid Steel)

(Fe-C System)

0 .7 6 C

0

pearlite Fe

3

C

 

 

v x V X

W

pearlite

= W

W

a

= X/(V + X)

W

Fe =(1 - W

a

)

3

C’

W

=(1-W

) W

=x/(v + x)

Fe

3

C

proeutectoid Fe

3

C

60 m Hypereutectoid steel

pearlite

Adapted from Figs. 9.24 and 9.32,Callister &

Rethwisch 8e. (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.)

(32)

Chapter 9 - 32

예제

99.6 wt% Fe-0.40 wt% C 강에 대하여 공석점 직하의 온도에서 다음을 결정하라:

a) Fe

3

C와 ferrite (a) 의 조성

b) 100 g의 강 중 cementite (in grams)의 양

c) 100 g 중 pearlite와 proeutectoid ferrite (a)의

(33)

Solution to Example Problem

W

Fe

3C

R

RSC

0

C

a

C

Fe

3C

C

a

 0.40  0.022

6.70  0.022  0.057

b) tie line에서 지렛대 원리 이용

a) 공석점 직하에서 RS tie line을 이용

C a = 0.022 wt% C C Fe

3

C = 6.70 wt% C

Fe

3

C ( c eme ntite)

1600 1400 1200 1000 800 600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

 + Fe

3

C

a + Fe

3

C

L+Fe

3

C

C , wt% C 1148ºC

T(ºC)

727ºC

C

0

R S

C

Fe C

C

a 3

100 g 중 Fe 3 C의 양

= (100 g)W Fe

3 C

= (100 g)(0.057) = 5.7 g

(34)

Chapter 9 - 34

Solution to Example Problem (cont.)

c) 공석점 직상의 온도에서 VX tie line를 이용

C

0

= 0.40 wt% C C a = 0.022 wt% C

C

pearlite

= C

= 0.76 wt% C

Fe

3

C ( c eme ntite)

1600 1400 1200 1000 800 600

400 0 1 2 3 4 5 6 6.7

L

(austenite)

 +L

 + Fe

3

C

a + Fe

3

C

L+Fe

3

C

C, wt% C 1148ºC

T(ºC)

727ºC

C

0

V X

C

C

a

W

pearlite

V

VXC

0

C

a

C

C

a

 0.40  0.022

0.76  0.022  0.512

100 g 중 pearlite의 양

= (100 g)W pearlite

= (100 g)(0.512) = 51.2 g

(35)

VMSE: Interactive Phase Diagrams

Microstructure, phase compositions, and phase fractions respond interactively

(36)

Chapter 9 - 36

Alloying with Other Elements

• T eutectoid changes:

Adapted from Fig. 9.34,Callister & Rethwisch 8e.

(Fig. 9.34 from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 127.)

T E utectoi d C)

wt. % of alloying elements

Ti

Ni

Mo Si

W

Cr Mn

• C eutectoid changes:

Adapted from Fig. 9.35,Callister & Rethwisch 8e.

(Fig. 9.35 from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals, 1939, p. 127.)

wt. % of alloying elements C eutec toid (w t% C)

Ni

Ti

Cr Si

W Mn

Mo

(37)

• Phase diagrams are useful tools to determine:

-- the number and types of phases present, -- the composition of each phase,

-- and the weight fraction of each phase

given the temperature and composition of the system.

• The microstructure of an alloy depends on

-- its composition, and

-- whether or not cooling rate allows for maintenance of equilibrium.

• Important phase diagram phase transformations include eutectic, eutectoid, and peritectic.

Summary

(38)

Chapter 9 - 38

Core Problems:

Self-help Problems:

ANNOUNCEMENTS

Reading:

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