Chapter 11: 상태도

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 11: 상태도

(Phase Diagrams)

Phase B Phase A

Nickel atom

Copper atom

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

40 60 80 100

W ater

• 고용체 – 고체, 액체, 기체상의 단상으로 구성

• 혼합 – 한 상 이상으로 구성

Adapted from Fig. 11.1,

Callister & Rethwisch 9e.

• 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.

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

D (100ºC, C = 90)

2 phases

B (100ºC, C = 70)

1 phase

A (20ºC,C = 70)

2 phases

Fig. 11.1, Callister &

Rethwisch 9e.

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

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)

Cu-Ni phase diagram

전율고용 2원계 상태도

(Isomorphous Binary Phase Diagram)

• Phase diagram:

Cu-Ni system.

• System is:

--

Cu와 Ni

-- 전율고용체(isomorphous)

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)

Fig. 11.3(a), Callister & Rethwisch 9e.

(Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, 1991. Reprinted by permission of ASM International, Materials Park, OH.)

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

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)

Fig. 11.3(a), Callister & Rethwisch 9e.

(Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, 1991. Reprinted by permission of ASM International, Materials Park, OH.)

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

35 C ₀ 32 C _L

_A = 1320ºC:

액상(L) 만이 존재

C

_L

₀ ( = 35 wt% Ni)

T

_B = 1250ºC:

두상 a 와 L 이 존재

C

_L = Cliquidus ( = 32 wt% Ni)

_a = Csolidus ( = 43 wt% Ni)

_D = 1190ºC:

고상(a) 만이 존재

C

_a

₀ ( = 35 wt% Ni) C ₀ = 35 wt% Ni의 조성

T

_D

tie line

4 C 3 _a

_B

Fig. 11.3(b), Callister & Rethwisch 9e.

(Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, 1991. Reprinted by permission of ASM International, Materials Park, OH.)

• 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

_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)

30 40 50

Cu-Ni system

T

_A

35 C ₀ 32 C _L

_B

T

_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 _L  S R + S

W _a  R R + S

C ₀ = 35 wt% Ni

Fig. 11.3(b), Callister & Rethwisch 9e.

(Adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash, Editor, 1991. Reprinted by permission of ASM International, Materials Park, OH.)

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

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 S  M _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)

30 40 50

TB B

tie line

C ₀

C _L

C a S

R

Adapted from Fig. 11.3(b),

Callister & Rethwisch 9e.

wt% Ni

20 120 0 130 0

30 40 50

110 0

L (liquid)

a (solid) T(ºC)

A

35 C ₀

L: 35wt%Ni

Cu-Ni system

• 상태도:

Cu-Ni system.

• 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

Adapted from Fig. 11.4,

Callister & Rethwisch 9e.

• 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 a의 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

기계적 성질: Cu-Ni System

• 고용체 강화의 영향:

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

T ensile S trengt h (MPa)

Composition, wt% Ni

Cu Ni

0 20 40 60 80 100 200

300 400

TS for pure Ni

TS for pure Cu

Elongation (% 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. 11.5(a), Callister & Rethwisch 9e.

Adapted from Fig. 11.5(b),

Callister & Rethwisch 9e.

2가지 조성

최소의 용해온도(T)를 갖는 특정 조성

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

• C _E 조성

Ex.: Cu-Ag system

Cu-Ag system

L (liquid) a L +

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} ^779ºC _{71.9 91.2}

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 ) Fig. 11.6, Callister & Rethwisch 9e

[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.].

Chapter 11 - 16

L+

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 =

Wb = C ₀ - C _a C _b - C _a R =

R+S

= 29

88 = 0.33

= 40 - 11 99 - 11 Answer:

Fig. 11.7, Callister & Rethwisch 9e.

[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in- Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

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+

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 = 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:

Fig. 11.7, Callister & Rethwisch 9e.

[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in- Chief), 1990. Reprinted by permission of ASM

• 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

300

100

L a

30

a + b

400

(room T solubility limit)

T

(Pb-Sn

System)

a L L: C

wt% Sn

a: C

wt% Sn

Fig. 11.10, Callister &

Rethwisch 9e.

• 2 wt% Sn < C ₀ < 18.3 wt% Sn 합금

• 결과:

a

+ b 구역 내의 온도

--

b-phase 입자를 갖는 다결정

공정계의 미세조직 II

Pb-Sn system L + a

200

T(ºC)

C, wt% Sn

10

18.3 20 0

C

300

100

L

a

30

a + b

400

(sol. limit at T ) T

2

(sol. limit at Troom)

L a L: C

wt% Sn

a b

a: C

wt% Sn

Fig. 11.11, Callister &

Rethwisch 9e.

• 합금의 조성: C ₀ = C _E

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

공정합금의 미세조직 III

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+

183ºC

40 T

18.3

a: 18.3 wt%Sn

97.8 b: 97.8 wt% Sn

C

61.9

L: C

wt% Sn

Fig. 11.12, Callister &

Rethwisch 9e.

Fig. 11.13, Callister & Rethwisch 9e.

(From Metals Handbook, 9th edition, Vol. 9, Metallography and Microstructures, 1985.

Reproduced by permission of ASM International, Materials Park, OH.)

Lamellar Eutectic Structure

Figs. 11.13 & 11.14, Callister & Rethwisch 9e.

(Fig. 11.13 from Metals Handbook, 9th edition, Vol. 9, Metallography and Microstructures, 1985. Reproduced by permission of ASM International, Materials Park, OH.)

• 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

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

L: C ₀ wt% Sn a L L

a

Fig. 11.15, Callister &

Rethwisch 9e.

L+ a

L+ b a + b

200

C, wt% Sn

20 60 80 100

0 300

100

L

a b

T

40

(Pb-Sn System)

아공석(Hypoeutectic) & 과공석(Hypereutectic)

160 m eutectic micro-constituent

hypereutectic: (illustration only)

b b b

b b

b

175 m

a a

a a a

a

hypoeutectic: C

= 50 wt% Sn

T(ºC)

61.9 eutectic

eutectic: C

= 61.9 wt% Sn

Fig. 11.16, Callister &

Rethwisch 9e. Fig. 11.13, Callister &

Adapted from Fig. 11.16, Callister & Rethwisch 9e.

(Figs. 11.13 and 11.16 from Metals Handbook, 9th ed., Vol. 9, Metallography and Microstructures, 1985.

Reproduced by permission of ASM International, Materials Park, OH.)

Fig. 11.7, Callister & Rethwisch 9e.

Massalski (Editor-in-Chief), 1990.

Reprinted by permission of ASM International, Materials Park, OH.]

금속간 화합물(Intermetallic Compounds)

Mg ₂ Pb

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

Fig. 11.19, Callister &

Rethwisch 9e.

[Adapted from Phase Diagrams of Binary Magnesium Alloys, A. A.

Nayeb-Hashemi and J. B.

Clark (Editors), 1988.

Reprinted by permission of ASM International, Materials Park, OH.]

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

heat

cool heat

• Peritectic – 액상과 고상이 다른 1개의 고상으로 상변화

S ₁ + L S ₂

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

Eutectoid & Peritectic

Cu-Zn Phase diagram

Fig. 11.20, Callister & Rethwisch 9e.

[Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 2, T. B. Massalski (Editor-in- Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Eutectoid transformation δ γ + e

Peritectic transformation γ + L δ

철-탄소 (Fe-C) 상태도

• 2 중요한 points

- Eutectoid (B):

  a +Fe ₃ C

- Eutectic (A):

L   + Fe

₃ C

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 = Teutectoid

120 m 0.76 4.30

B

   

A _L+Fe

3 C

Fe ₃ C (cementite-hard) a (ferrite-soft)

Fig. 11.26, Callister & Rethwisch 9e.

(From Metals Handbook, Vol. 9, 9th ed.,

Result: Pearlite = alternating layers of α and Fe

C phases

Fig. 11.23, Callister

& Rethwisch 9e.

[Adapted from Binary Alloy Phase Diagrams, 2nd edition,

Fe 3 C (c ementit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L γ

(austenite)

γ

^{+ Fe} ₃ ^C

α

^{+ Fe} ₃ ^C

L+Fe ₃ C

δ

(Fe) C, wt% C

1148°C

T(°C)

a ^727°C

(Fe-C System)

C₀

0. 76

아공석 강(Hypoeutectoid Steel)

Adapted from Figs. 11.23 and 11.28, Callister &

Rethwisch 9e.

[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B.

Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Adapted from Fig. 11.29, Callister & Rethwisch 9e.

proeutectoid ferrite pearlite

100 μm Hypoeutectoid steel α

pearlite

γ γ γ ^α γ

α α

γ γ γ γ

γ γ γ γ

Fe 3 C (c ementit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L γ

(austenite)

γ

^{+ Fe} ₃ ^C

α

^{+ Fe} ₃ ^C

L+Fe ₃ C

δ

(Fe) C, wt% C

1148°C

T(°C)

α

727°C

(Fe-C System)

C₀

0. 76

아공석 강(Hypoeutectoid Steel)

γ γ γ

α γ

α α

s r

W _α = s/(r + s) W _γ =(1 - W _α )

R S

α

pearlite

W _pearlite = W _γ W _{α ’} = S/(R + S) W _Fe =(1 – W _α’ )

3 C

proeutectoid ferrite pearlite

100 μm Hypoeutectoid steel

Adapted from Figs. 11.23 and 11.28, Callister &

Rethwisch 9e.

[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B.

Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Chapter 11 -

Fe 3 C (c ementit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L γ

(austenite)

γ

^{+ Fe} ₃ ^C

α

^{+ Fe} ₃ ^C

L+Fe ₃ C

δ

(Fe) C, wt% C

1148°C

T(°C)

α

727°C

(Fe-C System)

C₀

30

과공석 강(Hypereutectoid Steel)

0 .7 6 ^C

Fe

C

γγ γγ γγ γγ γγ γγ

Adapted from Fig. 11.32, Callister & Rethwisch 9e.

proeutectoid Fe ₃ C

60 μm Hypereutectoid steel

pearlite

pearlite

Adapted from Figs. 11.23 and 11.31, Callister &

Rethwisch 9e.

[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B.

Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Fe 3 C (c ementit e)

1600 1400 1200 1000 800

600

400 0 1 2 3 4 5 6 6.7

L γ

(austenite)

γ

^{+ Fe} ₃ ^C

α

^{+ Fe} ₃ ^C

L+Fe ₃ C

δ

(Fe) C, wt% C

1148°C

T(°C)

α

727°C

(Fe-C System)

C₀

proeutectoid Fe ₃ C

60 μm Hypereutectoid steel

pearlite

Adapted from Figs. 11.23 and 11.31, Callister &

Rethwisch 9e.

[Figure 9.24 adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B.

Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

과공석 강(Hypereutectoid Steel)

0 .7 6 ^C

pearlite Fe

C

γγ γγ

v x V X

W _pearlite = W _γ W _α = X/(V + X)

W _Fe =(1 - W _α )

3

C’

W =(1-W _γ ) W _γ =x/(v + x)

Fe

C

예제

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

a) Fe

₃

b) 100 g의 강 중 cementite (in grams)의 양

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

Solution to Example Problem



W _Fe

3

C  R

R  S  C ₀ C _a C _Fe

3

C 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 ementit e)

1600 1400 1200 1000 800 600

400 0 1 2 3 4 5 6 6.7

L



(austenite)

+L

 + Fe

C

a ^{+ Fe}

^C

L+Fe

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

Fig. 11.23, Callister & Rethwisch 9e.

[From Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T.

B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

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 ementit e)

1600 1400 1200 1000 800 600

400 0 1 2 3 4 5 6 6.7

L



(austenite)

+L

 + Fe

C

a ^{+ Fe}

^C

L+Fe

C



C, wt% C 1148ºC

T(ºC)

727ºC

C ₀ V X

C _ C _a



W _pearlite  V

V  X  C 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

Fig. 11.23, Callister & Rethwisch 9e.

[From Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T.

B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

VMSE: Interactive Phase Diagrams

Microstructure, phase compositions, and phase fractions respond interactively

Alloying with Other Elements

• T _eutectoid changes:

Fig. 11.33, Callister & Rethwisch 9e

(From Edgar C. Bain, Functions of the Alloying Elements in Steel, 1939. Reproduced by permission of ASM International, Materials Park, OH.)

T E utectoi d (º C )

wt. % of alloying elements

Ti

Ni

Mo Si

W

Cr Mn

• C _eutectoid changes:

Fig. 11.34,Callister & Rethwisch 9e.

(From Edgar C. Bain, Functions of the Alloying Elements in Steel, 1939. Reproduced by permission of ASM International, Materials Park, OH.)

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

Ni

Ti

Cr Si

W Mn

Mo

• 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

Summary

Core Problems:

Self-help Problems:

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