EMC 5719/5712 - Materiais e Microestruturas (/Fundamentos de Engenharia de Materiais 2), prof. Paulo Wendhausen. Curso de Engenharia de Materiais Departamento de Engenharia Mecânica Universidade Federal de Santa Catarina

1. Diagramas de Equilíbrio
e Transformacoes
Composicao + Processamento = Microestrutura + Propriedades
EMC5712-Materiais e Microestrutura
Prof. Wendhausen
Daphiny Pottmaier, posdoc
Fonte figuras: Callister 7ed.
Agosto & Dezembro 2011.

2. GOL
• Esbocar diagramas de fases simples (isomorfos,
euteticos e eutetoides);
• Identificar as regioes de fases, linhas liquidus-
solvus-solidus e pontos de coexistencia;
• Calcular composicoes das fases (linha de
amarracao) e fracoes massicas (regra da alavanca);
• Localizar as temperaturas e composicoes das
transformacoes (pontos/linhas);
• Escrever as reacoes para as transformacoes e
desenvolvimento das microestruturas.

3. Sumario
• Contextualizacao
• Introducao (aplicacao, limitacao)
• Diagramas de Fases/Equilibrio (X,T,P)
• Conceitos (componente, fase, sistema, solucao)
• Unario (H2O)
• Isomorfo (Cu-Ni)
• Eutetico (Pb-Sn)
• Eutetoide (Fe-C)
• Conceitos (difusiva/displaciva, cinetica)
• Diagramas Tempo-Temperatura-Transformacao

4. CONTEXTUALIZAÇÃO
• Aplicacao:
– Quimico-Fisica
– Engenharia
– Mineralogia
– Ciencia dos Materiais
• Limitacoes:
– Taxa de Transformacao
– TTT

5. INTRODUÇÃO
EXEMPLOS “PRÁTICOS” – Brasagem com ligas Pb-Sn

6. INTRODUÇÃO
EXEMPLOS “PRÁTICOS” - Brasagem de Chips de Si

7. Diagramas de Fases/Equilibrio
Mapas para Determinação da Microestrutura
Representação gráfica de dados:
 informações sobre os compostos puros
 natureza das interações entre mais de um componente
Informações disponíveis diretamente no diagrama:
 Tf de cada componente puro
 redução de Tf pela mistura de 2 ou mais componentes
 interação de dois componentes (Fe + C) para
formar um terceiro (Fe3C )
 presença e grau de solubilidade sólida
 efeito da temperatura na solubilidade sólida
 temperatura de transformação polimórfica
 quantidade e composição das fases líquidas e sólidas a
temperatura e composição química global específica
 presença de líquidos imiscíveis a altas temperaturas

8. DIAGRAMAS DE EQUILIBRIO
Representacoes graficas dos estados de equilibrio disponivel para
um sistema e a influencia dos estados de equilibrio com a
composicao (X), temperatura (T) e pressao (P).
Equilibrio se X, T e p sao
estaveis, nao muda com o tempo.
Descrito termodinamicamente
como o estado do sistema dado
pela minima energia livre (G).

9. CONCEITOS
Componente: elementos quimicos e compostos
estoiquiometricos (Al, H2O, Cu, Fe3C) 8
Chapter
Sistema: categorizado pelo numero de componentes
unario, binario, ternario, quaternario Chapter 8
Phase Diagrams
Fase: caracteristicas fisicasae quimicas (solidos),
A phase in a material is region that differ in its microstructure and
miscibilidade (liquidos) another region (gases)
or composition from e uniforme Phase Diagram
Homogeneo x Heterogeneo in a material is a region that differ in its mic
A phase
or composition from another region
Solucao: solvente e soluto
Limite de Solubilidade
Al2CuMg
Al2CuMg H2O(solid, ice) in H2O
Al
(liquid) ! 2 phases
H2O(so
Al
• homogeneous in crystal structure and atomic arrangement (liquid
• have same chemicalhomogeneous in crystal structure and atomic arra
• and physical properties throughout

10. DIAGRAMA UNARIO
composicao quimica fixa,
T e P variaveis
100 fusao
Liquido
congelamento
evaporacao
H2O
3 fases: solido,
condensacao
liquido, gas.
1 Solido
Pressao [atm]
Ponto triplo:
sublimacao
Gas 0.0098 °C,
deposicao
0.0063 atm.
0 100 Regiao: 1 fase
Temperatura [°C] Linha: 2 fases
SI: Kelvin, Pascal Ponto: 3 fases

11. DIAGRAMA UNARIO

12. ALOTROPIA
composicao
quimica fixa,
T e P variaveis
I - XV: alotropos
do gelo.
H2O

13. ENERGIA LIVRE
Gsolido
G [kJ/mol]
G(T,p)= H - T.S
H = Href + ∫CpdT
Gliquido
S = Sref + ∫CpdlnT
Ggas
H2O
0 100 Temperatura [°C]
P=1 atm

14. LEI DAS FASES DE GIBBS
Graus de liberdade (F) de um sistema fechado em equilibrio, em
termos de fases separadas (P) e componentes quimicos (C) e
variaveis do processo (N).
100
Liquido
F+P=C+N
(i)
H2O, C = 1
(ii)
1 Solido (iii) (i) P = 1, F = 2
(ii) P = 2, F = 1
Pressao [atm]
Gas
(iii) P = 3, F = 0
0 100 Temperatura [°C] F: freedom, P: phase

15. Solubility Limit: Water-Sugar
Solubilidade do Açúcar em Água
• Changing T can change # of phases: path A to B.
• Changing Co can change # of phases: path B to D
B (100,70) D(100,90)
1 phase 2 phases
10 0
80 L
(liquid)
Temperature (°C)
60 +
L S
(liquid solution (solid
40 i.e., syrup) sugar)
20 A(70, 20 ) T : B-D
2 phases C : B-A
0
0 20 40 60 70 80 10 0
C o =Composition (wt% sugar) Adapted from Callister
Chapter 8

16. Sistemas Eutéticos Binários
Concept Check 9.5
(SEM solubilidade no estadoO–NaClEx: NaCl-H2O)
Below is a portion of the H2 sólido phase diagram:
10 50
Liquid
(brine) 40
0
30
Salt
Temperature (°C)
Temperature (°C)
ϩ
Ice 20
Liquid
ϩ (brine)
Ϫ10
Liquid
(brine) 10
0
Ϫ20
Ϫ10
Ice ϩ Salt
Ϫ20
Ϫ30
NaCl 0 10 20 30
H2O 100 90 80 70
Composition (wt%)

17. SOLUBILIDADE SÓLIDA
ELEMENTOS PUROS
Regra Hume-Rothery:
•Razao raio atomico (± 15%)
•Estrutura cristalina
•Eletronegatividade (± 0.4 e.u.)
•Mesma Valencia

18. SOLUBILIDADE SÓLIDA
INTERSTICIAIS

19. DIAGRAMA - experimental "#!$%&'()*+!,-%!,)&%!./)0!1$'&!,-%!23$(%0!.*4!$%56.
23$(%0!)*4)2.,%!,-%!,%&5%$.,3$%0!'1!,-%!0'6)430!.*4!6
.66'70!,-%!0'6)430!.*4!6)93)430!,'!<%!56',,%4!,'!5$'43
!
!
)&%!./)0!1$'&!,-%!23$(%0!.*4!$%56.2)*+!),!7),-!2'&5'0),)'*8!,-%!2''6)*+!
%!,%&5%$.,3$%0!'1!,-%!0'6)430!.*4!6)93)430!1'$!.!+)(%*!2'&5'0),)'*:!;-)0!
!.*4!6)93)430!,'!<%!56',,%4!,'!5$'432%!,-%!5-.0%!4).+$.&=!
!
-%!,)&%!./)0!1$'&!,-%!23$(%0!.*4!$%56.2)*+!),!7),-!2'&5'0),)'*8!,-%!2''6)*+! !
!,-%!,%&5%$.,3$%0!'1!,-%!0'6)430!.*4!6)93)430!1'$!.!+)(%*!2'&5'0),)'*:!;-)0!
430!.*4!6)93)430!,'!<%!56',,%4!,'!5$'432%!,-%!5-.0%!4).+$.&=! !"#$%&#'&(&)#)*'&#
>1!.*!.66'#!2'*0)0,0!'1!&'$%!,-.*!'*%!5-.0%8!,-%!.&'
1'3*4!<#!.556#)*+!,-%!6%(%$!$36%!,'!,-%!5-.0%!4).+$.&
!
;-%!6%(%$!$36%!2.*!<%!%/56.)*%4!<#!2'*0)4%$)*+!.!0)&
.66'#!)0!$%5$%0%*,%4!<#!,-%!1362$3&!.*4!,-%!2'&5'0)
.!<.$:!;-%!5$'5'$,)'*0!'1!,-%!5-.0%0!5$%0%*,!.$%!4%,%
<.6.*2%!,-%!0#0,%&:!
!
! !

20. REGRA DA ALAVANCA
R Co S
α
L
Wα = S/(R+S) = Co - CL / Cα - CL
WL = R/(R+S) = Cα - Co / Cα - CL

21. SISTEMA ISOMORFO Cu-Ni 9.7 Binary Isomorphous Systems • 259
Figure 9.3 (a) The Composition (at% Ni)
copper–nickel phase
0 20 40 60 80 100
diagram. (b) A 1600
portion of the
copper–nickel phase 2800
diagram for which
1500
compositions and
phase amounts are Liquid 1453°C
determined at point 2600
B. (Adapted from 1400
Phase Diagrams of
Temperature (°C)
Temperature (°F)
Binary Nickel Alloys, Solidus line
P. Nash, Editor, 1991. Liquidus line
2400
1300 ␣ +L
Reprinted by
permission of ASM
B
International,
Materials Park, OH.) 1200 ␣
2200
1100 A 2000
1085°C
1000
0 20 40 60 80 100
(Cu) Composition (wt% Ni) (Ni)
(a)

22. 6T_c09_252-310 11/29/05 11:33 Page 265
REVISED PAGES
DIAGRAMA Cu-Ni
Composição9.9 Development das Fases -Isomorphous Alloys • 265
Química of Microstructure in Equilíbrio
Figure 9.4
Schematic
L
representation of the L L
development of (35 Ni) (35 Ni)
microstructure ␣ (46 Ni)
during the 1300 a ␣
equilibrium +
L
solidification of a
35 wt% Ni–65 wt%
Cu alloy.
L (32 Ni) b
␣ (46 Ni)
c
Temperature (°C)
␣ (43 Ni) ␣ (43 Ni)
L (24 Ni)
d ␣
␣
L (32 Ni) ␣ ␣
1200 ␣
e L (24 Ni)
␣ ␣
␣
␣ (35 Ni) ␣ ␣ ␣
␣
␣ ␣
␣
␣
␣
␣ ␣
␣
␣ (35 Ni) ␣
1100
20 30 40 50
Composition (wt% Ni)

23. DIAGRAMA BINÁRIO
SOLUÇÃO SÓLIDA TOTAL

24. MICROESTRUTURAS DE LIGAS
COM SOLUÇÃO SÓLIDA TOTAL

25. alloys are affected by composition as other structural variables (e.g., grain size) are
Sistemas Isomorfos
held constant. For all temperatures and compositions below the melting tempera-
ture of the lowest-melting component, only a single solid phase will exist. There-
fore, each component will experience solid-solution strengthening (Section 7.9), or
(Propriedades Mecânicas)
an increase in strength and hardness by additions of the other component. This
effect is demonstrated in Figure 9.6a as tensile strength versus composition for the
60
Elongation (% in 50 mm [2 in.])
60
400
Tensile strength (MPa)
50
Tensile strength (ksi)
50
40
300
40
30
200 30
20
0 20 40 60 80 100 0 20 40 60 80 100
(Cu) (Ni) (Cu) (Ni)
Composition (wt% Ni) Composition (wt% Ni)
(a) (b)
Figure 9.6 For the copper–nickel system, (a) tensile strength versus composition, and
(b) ductility (%EL) versus composition at room temperature. A solid solution exists over
all compositions for this system.

26. SISTEMA EUTÉTICO
SEM SOLUÇÃO SÓLIDA

27. MICROESTRUTURAS DE LIGAS
SEM SOLUÇÃO SÓLIDA

28. molten at about 185ЊC (365ЊF), which makes this material especially attractive as a
SISTEMA EUTETICO Pb-Sn
low-temperature solder, since it is easily melted.
Composition (at% Sn)
0 20 40 60 80 100
327°C
600
300
Liquid
500
232°C
␣ +L
Temperature (°C)
Temperature (°F)
200 ␣ ␤ +L 400
183°C
␤
18.3 61.9 97.8
300
100 ␣ + ␤ 200
100
0
0 20 40 60 80 100
(Pb) Composition (wt% Sn) (Sn)

29. tion at the point where ww¿ crosses the solidus line. The resulting alloy is poly-
crystalline with a uniform composition of C1, and no subsequent changes will occur
DIAGRAMA Pb-Sn
400 Figure 9.11 Schematic
L
representations of the
w
(C1 wt% Sn)
equilibrium microstructures for
␣
a lead–tin alloy of composition
a L
b L C1 as it is cooled from the
liquid-phase region.
300
Liquidus
c
␣ ␣
␣ +L
Temperature (°C)
␣ ␣
Solidus
200
(C1 wt% Sn)
␣
100
␣ +␤
wЈ
0 10 20 30
C1 Composition (wt% Sn)

30. MICROESTRUTURA MONOFÁSICA

31. (C3 in Figure 9.13). Consider an alloy having this composition that is cooled from
a temperature within the liquid-phase region (e.g., 250ЊC) down the vertical line yy¿
SISTEMA EUTETICO Pb-Sn
Figure 9.12 Schematic
representations of the
x equilibrium microstructures
L
d L for a lead–tin alloy of
(C2 wt% Sn) composition C2 as it is cooled
from the liquid-phase region.
300
L ␣
e
␣ ␣
␣ +L
Temperature (°C)
␣
200 ␣ ␣ C2 wt% Sn
f
␤
Solvus
line
g
␣
100
␣ +␤
xЈ
0 10 20 30 40 50
C2
Composition (wt% Sn)

32. 1496T_c09_252-310 1/9/06 13:00 Page 280
2nd REVISE PAG
DIAGRAMA Pb-Sn
280 • Chapter 9 / Phase Diagrams (liga hipoeutética)
L
(C4 wt% Sn)
z
j ␣ 600
300
L
␣ +L
L 500
␣ (18.3
wt% Sn) k
Temperature (°C)
Temperature (°F)
200 400
␤ +L
␣ l ␤
m
L (61.9 wt% Sn) Eutectic
structure 300
Primary ␣
␣ + ␤ (18.3 wt% Sn)
100
200
␤ (97.8 wt% Sn)
Eutectic ␣
(18.3 wt% Sn)
100
zЈ
0
0 20 60 80 100
(Pb) C4 (Sn)
(40)
Composition (wt% Sn)
Figure 9.16 Schematic representations of the equilibrium microstructures for a lead–tin

33. DIAGRAMA Pb-Sn
(liga hipoeutética)

34. Representação Esquemática
phase field. To distinguish one a from the other, that which resides in th
eutectic phase structure is called eutectic a, while the other that formed prior to cro
eutectic isotherm is termed primary a; both are labeled in Figure
primary phase
Reação Eutética
photomicrograph in Figure 9.17 is of a lead–tin alloy in which both prim
eutectic structures are shown.
Figure 9.15 Schematic represen
the formation of the eutectic str
␤ Pb the lead–tin system. Directions o
of tin and lead atoms are indicat
blue and red arrows, respectively
␣ Sn Liquid
␤ Pb
␣ Sn Eutectic
growth
direction
␤ Pb

35. apter 9 / Phase Diagrams DIAGRAMA Pb-Sn
gure 9.13
chematic
ations of 600
300 y L
uilibrium (61.9 wt%
res for a Sn)
n alloy of L 500
h
mposition ␣ +L
nd below
Temperature (°C)
Temperature (°F)
eutectic 200 ␣ 183°C
␤+L ␤ 400
perature. 18.3 i 97.8
300
100 ␣+␤
200
␣ (18.3 wt% ␤ (97.8 wt%
Sn) Sn)
100
yЈ
0
0 20 40 60 80 100
(Pb) C3 (Sn)
(61.9)
Composition (wt%Sn)

36. Microestrutura EUTETICA

37. ENERGIA LIVRE
H = Href + ∫CpdT S = Sref + ∫CpdlnT
γ 1400˚
G(T,p)= H - T.S
Fe3C
G [kJ/mol]
L
G
Gccc Gliquido Eutetico
1147˚
Gcfc
γ
L Fe3C
G
Fe L
T
γ
912 1394 1538 γ + Fe3C
α
α + Fe3C
Temperatura [°C]
P=1 atm Fe C
% Eutetico

38. austenite
912ЊC (1674ЊF). This austenite persists to 1394ЊC (2541ЊF), at which tem
SISTEMA EUTETOIDE Fe-C
the FCC austenite reverts back to a BCC phase known as d ferrite, whic
Composition (at% C)
0 5 10 15 20 25
1600
1538°C
1493°C
␦ L
1400
2500
1394°C ␥+L
1200
1147°C
Temperature (°C)
Temperature (°F)
2.14 4.30
␥, Austenite 2000
1000
912°C ␥ + Fe3C
800 ␣ 1500
+ 727°C
␥
0.76
0.022
600 ␣ + Fe3C
␣, Ferrite
Cementite (Fe3C) 1000
400
0 1 2 3 4 5 6 6.70
(Fe) Composition (wt% C)

39. Microestruturas Fe-C
9.18 The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram • 291
e 9.25
phs of
(90ϫ)
tenite
yright
nited
Steel
tion.)
(a) (b)
Microestrutura Ferrita α Microestrutura Austenita
melts at 1538ЊC (2800ЊF). All these changes are apparent along the left vertical axis
1

40. Section 9.12 and illustrated in Figure 9.16 for the eutectic system. Consider a com-
DIAGRAMA Fe-C
position C0 to the left of the eutectoid, between 0.022 and 0.76 wt% C; this is termed
hypoeutectoid alloy a hypoeutectoid (less than eutectoid) alloy. Cooling an alloy of this composition is
represented by moving down the vertical line yy¿ in Figure 9.29. At about 875ЊC ,
(liga hipoeutetoide)
point c, the microstructure will consist entirely of grains of the g phase, as shown
1100 Figure 9.29 Schematic
␥
representations of the
␥
microstructures for an
␥
␥ iron–carbon alloy of
1000
␥ hypoeutectoid composition C0
␥ + Fe3C (containing less than 0.76 wt%
y ␥
M
␥ C) as it is cooled from within
900 the austenite phase region to
␥ ␣
c ␥ below the eutectoid
temperature.
Temperature (°C)
␥
800 ␥
d
␥ ␥
e
Te N
f O
700
␣ Pearlite
600 Fe3C
Proeutectoid ␣
Eutectoid ␣
500 ␣ + Fe3C
yЈ
400
0 1.0 2.0
C0 Composition (wt% C)

41. from grain to grain; some of the pearlite appears dark because the many close
spaced layers are unresolved at the magnification of the photomicrograph. The
MICROESTRUTURA HIPOEUTETOIDE
0
h
C
a
e
e
d Proeutectoid
ϫ. ferrite
h
c
.)
Pearlite

42. Representação Esquemática
Reação Eutetoide
9.19 Development of Microstructure in Iron–Carbo
Austenite grain Figure 9.28
boundary
representatio
formation of
austenite; dir
␣ diffusion ind
Ferrite (␣)
Austenite
(␥ )
Austenite Ferrite (␣)
(␥ )
Ferrite (␣)
Cementite Growth direction
(Fe3C) Ferrite (␣) of pearlite
␣
Carbon diffusion

43. phase field (Figure 9.24) are relatively complex and similar to those described for
the eutectic systems in Section 9.12. Consider, for example, an alloy of eutectoid
DIAGRAMA Fe-C
composition (0.76 wt% C) as it is cooled from a temperature within the g phase re-
gion, say, 800ЊC—that is, beginning at point a in Figure 9.26 and moving down the
1100 Figure 9.26 Schematic
representations of the
microstructures for an
iron–carbon alloy of eutectoid
1000 ␥
␥ + Fe3C composition (0.76 wt% C) above
and below the eutectoid
temperature.
900
x ␥ ␥
Temperature (°C)
␥
800 a ␥
␣ +␥
727°C
b ␣
700
␣
600
Fe3C
500 ␣ + Fe3C
xЈ
400
0 1.0 2.0
Composition (wt% C)

44. MICROESTRUTURA EUTETOIDE

45. 2nd REVISE PAGE
DIAGRAMA Fe-C
298 • Chapter 9 / Phase Diagrams (liga hipereutetoide)
1100
P
Figure 9.32 Schematic
representations of the
␥ + Fe3C microstructures for an
iron–carbon alloy of
1000 ␥
z hypereutectoid composition
␥
␥ C1 (containing between 0.76
␥
g and 2.14 wt% C), as it is
␥
900 cooled from within the
Fe3C austenite phase region to
␥ below the eutectoid
␥ temperature.
Temperature (°C)
800 ␥
h
␥
␣ +␥
O i
700
␣
Pearlite
600 ␣
Proeutectoid
Fe3C Eutectoid Fe3C
500
␣ + Fe3C
z'
400
0 1.0 2.0
C1
Composition (wt% C)

46. MICROESTRUTURA of Microstructure in Iron–Carbon A
9.19 Development HIPEREUTETOIDE
gure 9.33
crograph
4 wt% C
having a
structure
f a white
eutectoid
network
nding the Proeutectoid
cementite
colonies.
opyright
y United
tes Steel
oration.)
Pearlite

47. REAÇÃO EUTETÓIDE
Sistema Fe-C

48. REAÇÃO EUTETÓIDE
Sistema Fe-C
MEV MO

49. Sistema Ferro-Carbono
Digrama de Equilíbrio

50. Ferro-Fundido Branco
Sistema Fe-C

51. Sistema Ferro-Carbono
Digrama de Equilíbrio

52. Ferro-Fundido Cinzento
Sistema Fe-C

53. eutectoid reaction but also the relative fra
Influencia de outros Elementos phase that form. Steels are normally alloy
either to improve their corrosion resistan
treatment (see Section 11.8).
9.20 The Influence of Other Alloying Elements • 301
Figure 9.34 The dependence of Figu
Ti 2400
0.8 eutectoid temperature on alloy com
Mo W Ni
1200 2200 concentration for several alloying for
Eutectoid temperature (°C)
Eutectoid temperature (°F)
Eutectoid composition (wt% C)
Si
elements in steel. (From Edgar C. Edg
2000 0.6
Bain, Functions of the Alloying Elem
1000 American Society 1939
Elements in Steel,Cr
1800
Cr
1600 0.4 for Metals, 1939, p. 127.)
800 Si
1400 Mo Mn
0.2 W
Mn 1200 Ti
600
Ni 1000
0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Concentration of alloying elements (wt%) Concentration of alloying elements (wt%)
Temperatura Eutetoide Composicao Eutetoide
existence at room temperature of nonequilibrium phases that do not appear on the

54. required for the transformation to proceed halfway to completion, t0.5, or
Transformation
rate—reciprocal of 1
rate ϭ (10.18)
the halfway-to- t0.5
TEMPO-TEMPERATURA-TRANSFORMAÇÃO
completion
transformation time Temperature will have a profound influence on the kinetics and thus on the
10_311-357 11/30/05 7:37 Page 323 rate of a transformation. This is PAGES
REVISED demonstrated in Figure 10.11, where y-versus-log t
100
:37 Page 323
termodinamicamente REVISED PAGES
Percent recrystallized
80
como o estado do sistema The Kinetics of Phase Transformations • 323
10.3
60 135ЊC 119ЊC 113ЊC 102ЊC 88ЊC 43ЊC
dado pela minima energia 1.0
Figure 10.10 Plot of fraction
reacted versus the logarithm of
40
time typical of many solid-state 20
livre (G).
Fraction of transformation, y
transformations in which
temperature is held constant. 0
2
104
10.3 The Kinetics of Phase Transformations • 323
1 10 10
Time (min)
0.5
(Logarithmic scale)
1.0 Figure 10.11 Percent recrystallization as a function of time and at constant
Figure 10.10 Plot of fraction
temperature for pure copper. (Reprinted with permission from Metallurgical
Representacoes graficas dos
t0.5
reacted versus the logarithm of
Transactions, Vol. 188, 1950, a publication of The Metallurgical Society of AIME,
time typical of many solid-state
Warrendale, PA. Adapted from B. F. Decker and D. Harker, “Recrystallization in Rolled
Fraction of transformation, y
0
Nucleation
estados da CINETICA de
Growth
transformations in which
Copper,” Trans. AIME, 188, 1950, p. 888.)
temperature is held constant.
transformacao para um sistema
Logarithm of heating time, t
formed material versus the logarithm of time; an S-shaped emsimilar to that in do tempo (t).
curve funcao
0.5 of which is distinctive of the new phase. Data are plotted as the fraction of trans-
Figure 10.10 represents the typical kinetic behavior for most solid-state reactions.
Nucleation and growth stages are also indicated in the figure.
For solid-state transformations displaying the kinetic behavior in Figure 10.10,
the fraction of transformation y is a function of time t as follows:
t0.5 y ϭ 1 Ϫ exp1Ϫkt 2
Avrami equation— n
dependence of (10.17)
fraction 0
of
transformation where k and n are time-independent constants for the particular reaction. The above
on time Nucleation
expression is often Growth to as the Avrami equation.
referred
By convention, the rate of a transformation is taken as the reciprocal of time
required for the of heating time, tproceed halfway to completion, t0.5, or
Logarithm transformation to
Transformation
rate—reciprocal of 1
rate ϭ (10.18)

55. CONCEITOS
Transformacao de fase: difusiva ou displaciva.
Difusiva: solidificacao, alotropicas, recristalizacao,
crescimento de grao, etc.
Ponto de vista microestrutural:
Nucleacao: Homogenea x Heterogenea
Crescimento:
Displaciva/martensitica: sem difusao, metaestavel.
Cinetica: velocidade (tempo) - mecanismo.

56. ters 10 and 11.
system has been chosen because it is familiar and because a wide variety
crostructures and mechanical properties are possible for iron–carbon (or steel)
9.18 THE IRON–IRON CARBIDE (Fe–Fe3C)
Diagrama TTT Fe-C eutetoide
PHASE DIAGRAM
10.5 ISOTHERMAL TRANSFORMATION DIAGRAMS diagram is presented in Figure
A portion of the iron–carbon phase
Pearlite upon heating, experiences two changes in crystal structure before it
ferrite temperature the stable form, called ferrite, or a iron, has a BCC c
ter 10 / Phase Transformations in Metals Consider again the
austenite
iron–iron carbide eutectoid reaction
Ferrite experiences a polymorphic transformation to FCC austeni
912ЊC (1674ЊF). This austenite persists to 1394ЊC (2541ЊF), at whi
Eutectoid reaction the FCC austenite reverts back to a BCC phase known as d ferrit
cooling
for the iron-iron
100 carbide system Figure 10.13 ∆ a10.022 wt% C2 ϩ Fe3C16.70 wt% C2 (1
g10.76 wt% C2
heating
transformed to pearlite
Demonstration of how Composition (at% C)
Percent of austenite
Transformation Transformation
which is fundamental to the development of microstructure in steel alloys.
an isothermal 5
0 10 15 20 25
temperature 675°C ends 1600
cooling, austenite, having an intermediate carbon concentration, transforms to
1538°C
50
transformation diagram1493°C
rite phase, having a much lower carbon content, and also cementite, with a
(bottom)␦ is generated L
higher carbon concentration. Pearlite is one microstructural product of this
1400
2500
Transformation from percentage ␥ + L
formation (Figure1394°C and the mechanism of pearlite formation was disc
9.27),
begins previously (Section 9.19) and demonstrated in Figure 9.28.
transformation-versus- 1147°C
1200
Temperature plays an important role in the rate of the austenite-to-pe
0 logarithm Austenite
␥, of time
105 transformation. The temperature dependence for an iron–carbon alloy of2000 eute
Temperature (°C)
2.14 4.30
1 10 102 103 104
measurements (top).
composition is indicated in Figure 10.12, which plots S-shaped curves of the
1000
Time (s) centage transformation versus the logarithm of time at three different tempera
[Adapted from H.
912°C ␥ + Fe C 3
For each curve, data were collected after rapidly cooling a specimen compos
Boyer, ␣
800 (Editor), Atlas
100% austenite to the temperature indicated; that temperature was maintained
+
1500
727°C
of Isothermal ␥
stant throughout the course of the reaction.
0.76
1400 A more convenient way of representing both the time and temperatur
Austenite (stable) Eutectoid temperature Transformation and 0.022
pendence of600 transformation is in the+ bottom portion of Figure 10.13. Her
this ␣, Ferrite ␣ Fe C 3
Austenite Cooling Transformation
vertical and horizontal axes are, respectively, temperature and the logarithm of
Cementite (Fe C) 1000 3
700
(unstable) Diagrams, American
Two solid curves are plotted; one represents the time required at each temper
400
initiation for Metals,21977, 3
0 1 4
1200 the Society or start of the transformation; C) other is for the transform
for (Fe) Composition (wt%
the 5 6 6.70
Pearlite conclusion. The dashed curve 9.24 The iron–iron carbide phase transformation compl
Figure corresponds to 50% of diagram. [Adapted from Binary
Temperature (°C)
Temperature (°F)
p. 369.]
These curves were generated from a series of T. B. Massalski (Editor-in-Chief), 1990. Repr
Diagrams, 2nd edition, Vol. 1, plots of the percentage transfo
600 permission of ASM International, Materials Park, OH.]
tion versus the logarithm of time taken over a range of temperatures. The S-sh
50% Completion curve
curve [for 675ЊC (1247ЊF)], in the upper portion of Figure 10.13, illustrates ho
1000
data transfer is made.
In interpreting this diagram, note first that the eutectoid temperature [
500 Completion curve
(~100% pearlite) (1341ЊF)] is indicated by a horizontal line; at temperatures above the eutecto
Begin curve 800 100 0 Figure 10.12 For
(~ 0% pearlite) iron–carbon alloy
400 eutectoid composi
(0.76 wt% C),
isothermal fractio
cent austenite
102 103 104 105
rcent pearlite
1 10 reacted versus the
Time (s) 50 600°C 650°C 675°C 50 logarithm of time
the austenite-to-p

57. 2nd REVISE PAGES
system has been chosen because it is familiar and because a wide variety
crostructures and mechanical properties are possible for iron–carbon (or steel)
Diagrama TTT Fe-C (perlita) 10.5 ISOTHERMAL TRANSFORMATION DIAGRAMS
Pearlite
Consider again the iron–iron carbide eutectoid reaction
Eutectoid reaction
10.5 Isothermal Transformation Diagrams a10.022327C2 ϩ Fe3C16.70 wt% C2
for the iron-iron g10.76 wt% C2 ∆ • wt%
cooling
(1
carbide system heating
1s 1 min which is fundamental to the development of microstructure in steel alloys.
1h 1 day
cooling, austenite, having an intermediate carbon concentration, transforms to
rite phase, having a much lower carbon content, and also cementite, with a
Eutectoid 1400
A ␥ Austenite (stable) higher carbon concentration. Pearlite is one microstructural product of this
temperature
727°C formation (Figure 9.27), and the mechanism of pearlite formation was disc
previously (Section 9.19) and demonstrated in Figure 9.28.
Temperature plays an important role in the rate of the austenite-to-pe
700 ␥ ␥ ␥ ␥ transformation. The temperature dependence for an iron–carbon alloy of eute
composition is indicated in Figure 10.12, which plots S-shaped curves of the
␥ ␥ ␣ Ferrite transformation versus the logarithm of time at three different tempera
centage Coarse pearlite
For each curve, data were collected after rapidly cooling a specimen compos
100% austenite to the temperature indicated; that temperature was maintained
1200
C stant throughout the course of the reaction.
Temperature (°C)
Temperature (°F)
A more convenient way of representing both the time and temperatur
B D pendence of this transformation is in the bottom portion of Figure 10.13. Her
600 Fe3C
vertical and horizontal axes are, respectively, temperature and the logarithm of
Two solid curves are plotted; one represents the time required at each temper
for the initiation or start of the transformation; the other is for the transform
Fine pearlite conclusion. The dashed curve corresponds to 50% of transformation compl
These curves were generated from a series of plots of the percentage transfo
tion versus the logarithm of time taken over a range of temperatures. The S-sh
1000
curve [for 675ЊC (1247ЊF)], in the upper portion of Figure 10.13, illustrates ho
data transfer is made.
Austenite → pearlite
500
transformation Denotes thatinterpreting this diagram, note first that the eutectoid temperature [
In a transformation
(1341ЊF)] is indicated by a horizontal line; at temperatures above the eutecto
is occurring
100 0 Figure 10.12 For
iron–carbon alloy
800 eutectoid composi
(0.76 wt% C),
1 10 102 103 104 105 isothermal fractio
cent austenite
rcent pearlite
reacted versus the
Time (s) 50 600°C 650°C 675°C 50 logarithm of time
the austenite-to-p

58. REAÇÃO EUTETÓIDE - Perlita
8 • Chapter 10 / Phase Transformations in Metals Sistema Fe-C
Figure 10.15
otomicrographs of
(a) coarse pearlite
d (b) fine pearlite.
00ϫ. (From K. M.
Ralls et al., An
Introduction to
terials Science and
Engineering, p. 361.
pyright © 1976 by
ohn Wiley & Sons,
w York. Reprinted
by permission of
ohn Wiley & Sons,
Inc.)
Perlita Grosseira Perlita Fina
For iron–carbon alloys of other compositions, a proeutectoid phase (either
ferrite or cementite) will coexist with pearlite, as discussed in Section 9.19. Thus
additional curves corresponding to a proeutectoid transformation also must be in-