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
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
• 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.
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
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
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)
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)
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).
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
LT 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
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 L S R + S
W a R 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).
• 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
aM
LR S
M
ax S M
Lx 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.
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
• 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
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.
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
ET 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 )
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
0C
b- C
a= 99 - 40
99 - 11 = 59
88 = 0.67 S
R+S =
W b = C
0- C
aC
b- C
aR =
R+S
= 29
88 = 0.33
= 40 - 11 99 - 11 Answer:
Adapted from Fig. 9.8, Callister & Rethwisch 8e.
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
0C
L- C
a= 46 - 40 46 - 17
= 6
29 = 0.21
W L = C
0- C
aC - 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.
Chapter 9 - 18
• C 0 < 2 wt% Sn의 합금
• 결과: 상온
-- C
0의 조성을 갖는 a phase 결정으로 구성된 다결정
공정계의 미세조직 I
0
L + a
200
T(ºC)
C , wt% Sn
10 2
20 C
0300
100
L a
30
a + b
400
(room T solubility limit)
T
E(Pb-Sn
System)
a L L: C
0wt% Sn
a: C
0wt% Sn
Adapted from Fig. 9.11, Callister & Rethwisch 8e.
• 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
0300
100
L
a
30
a + b
400
(sol. limit at T
E) T
E2
(sol. limit at T room )
L a L: C
0wt% Sn
a b
a: C
0wt% Sn
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
E18.3
a: 18.3 wt%Sn
97.8 b: 97.8 wt% Sn
C
E61.9
L: C
0wt% Sn
Lamellar Eutectic Structure
Adapted from Figs. 9.14 & 9.15, Callister
& Rethwisch 8e.
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
EL: C 0 wt% Sn a L L
a
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
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.
• 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)
Chapter 9 - 26
Eutectoid & Peritectic
Cu-Zn Phase diagram
Adapted from Fig. 9.21, Callister & Rethwisch 8e.
Eutectoid transformation +
Peritectic transformation + L
Chapter 9 - 27
철-탄소 (Fe-C) 상태도
• 2 중요한 points
- Eutectoid (B):
a + Fe
3C
- Eutectic (A):
L + Fe
3C
Adapted from Fig. 9.24, Callister & Rethwisch 8e.
Fe
3C (c ementit e)
1600 1400 1200
1000 800
600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+Fe
3C
a +Fe
3C
(Fe) C, wt% C
1148ºC
T(ºC)
a 727ºC = T eutectoid
4.30
Result: Pearlite = alternating layers of a and Fe
3C phases
120 m
(Adapted from Fig. 9.27, Callister & Rethwisch 8e.)
0.76
B
A L+Fe
3
C
Fe
3C (cementite-hard)
a (ferrite-soft)
Chapter 9 - 28
Fe
3C (c emen tit e)
1600 1400 1200 1000 800
600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+ Fe
3C
a + Fe
3C
L+Fe
3C
(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
Fe
3C (c emen tit e)
1600 1400 1200 1000 800
600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+ Fe
3C
a + Fe
3C
L+Fe
3C
(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
Chapter 9 - 30
과공석 강(Hypereutectoid Steel)
Fe
3C (c emen tit e)
1600 1400 1200 1000 800
600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+Fe
3C
a +Fe
3C
L+Fe
3C
(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
0Fe
3C
Adapted from Fig. 9.33, Callister & Rethwisch 8e.
proeutectoid Fe
3C
60 m Hypereutectoid steel
pearlite
pearlite
Fe
3C (c emen tit e)
1600 1400 1200 1000 800
600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+Fe
3C
a +Fe
3C
L+Fe
3C
(Fe) C, wt%C
1148ºC
T(ºC)
a
과공석 강(Hypereutectoid Steel)
(Fe-C System)
0 .7 6 C
0pearlite Fe
3C
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
3C
proeutectoid Fe
3C
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.)
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 조성b) 100 g의 강 중 cementite (in grams)의 양
c) 100 g 중 pearlite와 proeutectoid ferrite (a)의 양
Solution to Example Problem
W
Fe3C
R
R S C
0 C
aC
Fe3C
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
3C ( c eme ntite)
1600 1400 1200 1000 800 600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+ Fe
3C
a + Fe
3C
L+Fe
3C
C , wt% C 1148ºC
T(ºC)
727ºC
C
0R S
C
Fe CC
a 3100 g 중 Fe 3 C의 양
= (100 g)W Fe
3 C
= (100 g)(0.057) = 5.7 g
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
3C ( c eme ntite)
1600 1400 1200 1000 800 600
400 0 1 2 3 4 5 6 6.7
L
(austenite)
+L
+ Fe
3C
a + Fe
3C
L+Fe
3C
C, wt% C 1148ºC
T(ºC)
727ºC
C
0V X
C
C
a
W
pearlite V
V X C
0 C
aC
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
VMSE: Interactive Phase Diagrams
Microstructure, phase compositions, and phase fractions respond interactively
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 (º 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
• 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
Chapter 9 - 38