Chapter 10: Phase Transformations
ISSUES TO ADDRESS... • Transforming one phase into another takes time.
Fe Fe C Eutectoid 3 g transformation (cementite) (Austenite) + a C FCC (ferrite) (BCC)
• How does the rate of transformation depend on time and T? • How can we slow down the transformation so that we can engineering non-equilibrium structures? • Are the mechanical properties of non-equilibrium structures better? Chapter 10 - 1 Phase transformation
• Takes time (transformation rates: kinetics). • Involves movement/rearrangement of atoms. • Usually involves changes in microstructure
1. “Simple” diffusion-dependent transformation: no change in number of compositions of phases present (e.g. solidification of pure elemental metals, allotropic transformation, recrystallization, grain growth).
2. Diffusion-dependent transformation: transformation with alteration in phase composition and, often, with changes in number of phases present (e.g. eutectoid reaction).
3. Diffusionless transformation: e.g. rapid T quenching to “trap” metastable phases.
Chapter 10 - 2 º
TR = recrystallization temperature
TR
Adapted from Fig. 7.22, Callister 7e. The influence of annealing T on the tensile strength and ductility of a brass alloy.
º Chapter 10 - 3 Iron-Carbon Phase Diagram Eutectoid cooling: cool g (0.76 wt% C) a (0.022 wt% C) + Fe3C (6.7 wt% C) T(°C) heat 1600 d 1400 L g g+L 1200 A L+Fe C (austenite) 1148°C 3 R S 1000 g g g+Fe C g g 3 800a B 727°C = Teutectoid
R S (cementite) C 3 600 a+Fe C
3 Fe 400 0 1 2 3 4 5 6 6.7 0.76 4.30 (Fe) Co, wt% C Fe3C (cementite-hard)
a (ferrite-soft) eutectoid Adapted from Fig. 9.24,Callister 7e. C Chapter 10 - 4 Phase Transformations
Nucleation – nuclei (seeds) act as template to grow crystals – for nucleus to form rate of addition of atoms to nucleus must be faster than rate of loss – once nucleated, grow until reach equilibrium Driving force to nucleate increases as we increase T – supercooling (eutectic, eutectoid) – superheating (peritectic)
Small supercooling few nuclei - large crystals Large supercooling rapid nucleation - many nuclei, small crystals
Chapter 10 - 5 Solidification: Nucleation Processes • Homogeneous nucleation – nuclei form in the bulk of liquid metal – requires supercooling (typically 80-300°C max) • Heterogeneous nucleation – much easier since stable “nucleus” is already present • Could be wall of mold or impurities in the liquid phase – allows solidification with only 0.1-10ºC supercooling
Chapter 10 - 6 Phase 1 (e.g. liquid) Nucleation of 2nd phase Growth Homogeneous Nucleation
Thermodynamic parameters:
• Free energy G (or Gibbs free energy)
• Enthalpy H: internal energy of the system and the product of its volume multiplied by the pressure
• Entropy S: randomness or disorder of the atoms or molecules
ΔG is important---a phase transformation will occur spontaneously only when ΔG has a negative value.
ΔG = ΔH - TΔS
Chapter 10 - 7 Homogeneous Nucleation
Chapter 10 - 8 Homogeneous Nucleation & Energy Effects Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) 2 GS 4r g g = surface energy Activation Free Energy
GT = Total Free Energy = GS + GV
Volume (Bulk) Free Energy – stabilizes the nuclei (releases energy) 4 G r 3G V 3 volume free energy G unit volume r* = critical nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)
Adapted from Fig.10.2(b), Callister 7e. Chapter 10 - 9 Kinetics of solid state reactions
Critical nucleus size (rc) and the activation energy (G*) 4 G = r3G 4r 2g 3 v
Take the derivative and set equal to zero to find max. d(G) 4 (G )(3r 2 ) 4g (2r) 0 dr 3 v 2g rc Gv Substitution in to overall G equation 3 * 16g G 2 3(Gv ) Chapter 10 -10 The volume free energy change is the driving force for the solidification transformation Kinetics of solid state reactions
In terms of latent heat of fusion Hf (i.e. energy release upon solidification): H (T T) f m Tells us how Gv changes with temperature Gv Equilibrium Tm solidification temperature With this definition, we then have: T1 > T2 2g T m rc H f Tm T
2 16g 3 T G* m 2 3H f Tm T
As T decreases both rc * * G and G* become smaller Number of stable nuclei: n exp kT Chapter 10 - 11 LIQUID INSTABILITY at LOWER TEMPERTURES Solidification
r* = critical radius 2gT r* m g = surface free energy H T S Tm = melting temperature
HS = latent heat of solidification
T = Tm - T = supercooling
Note: HS = strong function of T g = weak function of T
r* decreases as T increases
For typical T r* ca. 100Å
Chapter 10 -12 Kinetics of solid state reactions
We also need to consider diffusion: • Faster diffusion leads to more collisions between atoms. • More collisions means higher probability of atoms sticking to each other.
Recall diffusion Qd D Do exp kT
Then, the frequency of atoms sticking together is directly related to diffusion:
Qd Frequency of attachment: vd exp kT
Chapter 10 -13 Kinetics of solid state reactions
Combining liquid instability and diffusion effects together:
Rate of Nucleation (units: nuclei per unit volume per second)
dN G* Qd Kn*vd K'exp exp Contribution from Contribution from dt kT kT liquid instability diffusion
G* Q n* exp v exp d Net rate kT d kT rate Nucleation
Liquid instability Diffusion Tm T
Chapter 10 -14 Example problem: critical radius and activation energy for nucleation
A) If pure liquid gold is cooled to 230oC below its melting point, calculate the critical radius and the activation energy. Values for the latent heat of fusion and surface free energy are -1.16x109J/m3 and 0.132J/m2, respectively.
2g T m 2 rc 3 H f Tm T 16g T G* m 2 3H f Tm T 1.32nm 9.64x10-19J B) Calculate the number of atoms per nucleus of this critical size. Au is FCC with a = 0.413nm. 4 r *3 critical nucleus volume # unit cells/particle 3 137 unit cell volume a3 4 atoms/unit cell……548 atoms/critical nucleus Chapter 10 -15 Rate of Phase Transformations
Kinetics – time dependence of nucleation, growth and transformation rates. • Hold temperature constant & measure transformation vs. time How is transformation measured? • microscopic examination X-ray diffraction – have to do many samples electrical conductivity – follow one sample sound waves – one sample
Chapter 10 -16
Rate of Phase Transformation y
All out of material - done Fixed T
0.5 maximum rate reached – now amount unconverted decreases so rate slows rate increases as surface area increases
t0.5 & nuclei grow Fraction transformed, transformed, Fraction log t Adapted from Fig. 10.10, Callister 7e. Avrami rate equation => y = 1- exp (-ktn) fraction time transformed – k & n fit for specific sample
By convention r = 1 / t0.5 Chapter 10 -17 Rate of Phase Transformations Cu
Adapted from Fig. 10.11, Callister 7e. (Fig. 10.11 adapted 135C 119C 113C 102C 88C 43C from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.) 1 10 102 104
• In general, rate increases as T -Q/RT r = 1/t0.5 = A e
– R = gas constant Arrhenius – T = temperature (K) expression – A = preexponential factor – Q = activation energy r equilibrium not possible! • often small: Chapter 10 -18 Eutectoid cooling: cool g (0.76 wt% C) a (0.022 wt% C) heat + Fe3C (6.7 wt% C)
Chapter 10 -19 Eutectoid Transformation Rate
• Growth of pearlite from austenite: Diffusive flow of C needed Austenite (g) cementite (Fe3C) grain a Ferrite (a) a boundary a g g g a g Adapted from a pearlite a a Fig. 9.15, growth Callister 7e. a direction a
• Recrystallization 100 600°C rate increases (T larger) 650°C with T. 50 Adapted from 675°C Fig. 10.12,
(T smaller) Callister 7e. (% pearlite) (%
y 0
Course pearlite formed at higher T - softer Fine pearlite formed at low T - harder Chapter 10 -20 Nucleation and Growth • Reaction rate is a result of nucleation and growth of crystals. 100 Nucleation rate increases with T % Pearlite Growth regime Growth rate increases with T 50 Nucleation regime Adapted from 0 t0.5 log (time) Fig. 10.10, Callister 7e. • Examples: pearlite g colony g g
T just below TE T moderately below TE T way below TE Nucleation rate low Nucleation rate med . Nucleation rate high Growth rate high Growth rate med. Growth rate low
Chapter 10 -21 Transformations & Undercooling
• Eutectoid transf. (Fe-C System): g a + Fe3C • Can make it occur at: 0.76 wt% C 6.7 wt% C ...727ºC (cool it slowly) 0.022 wt% C ...below 727ºC (“undercool” it!) T(°C) 1600 Adapted from Fig. d 9.24,Callister 7e. (Fig. 9.24 1400 L adapted from Binary Alloy Phase Diagrams, 2nd ed., g g+L Vol. 1, T.B. Massalski (Ed.- 1200 1148°C L+Fe C in-Chief), ASM International, (austenite) 3 Materials Park, OH, 1990.) 1000 +Fe C a Eutectoid: g 3 ferrite 800 Equil. Cooling: Ttransf. = 727ºC 727°C
T (cementite) C a +Fe3C 3 600 Undercooling by T < 727C transf. Fe
400 0.76 0 0.022 1 2 3 4 5 6 6.7 (Fe) Co, wt%C
Chapter 10 -22 Isothermal Transformation Diagrams T-T-T plots • Fe-C system, Co = 0.76 wt% C • Transformation at T = 675°C. T: hold constant
100
T = 675°C , , y 50
0 % % transformed 1 102 104 time (s) Only for Fe-C alloy of T(°C) Austenite (stable) eutectoid composition T (727C) 700 Austenite E (unstable) Pearlite 600 Adapted from Fig. 10.13,Callister 7e. isothermal transformation at 675°C (Fig. 10.13 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and 500 Cooling Transformation Diagrams, American Society for Metals, 1977, p. 400 369.) 2 3 4 5 time (s) 1 10 10 10 10 10 Chapter 10 -23 Effect of Cooling History in Fe-C System • Eutectoid composition, Co = 0.76 wt% C • Begin at T > 727°C • Rapidly cool to 625°C and hold isothermally.
T(°C) A Austenite (stable) TE (727C) 700 Austenite (unstable) C D B Adapted from Fig. 600 Pearlite 10.14,Callister 7e. g g (Fig. 10.14 adapted from H. Boyer (Ed.) Atlas of g g g g Isothermal Transformation 500 and Cooling Transformation Diagrams, American Society for Metals, 1997, p. 28.) 400
1 10 102 103 104 105 time (s) Chapter 10 -24 Pearlite
Coarse (quenched to higher T) Fine (quenched to lower T) Chapter 10 -25 Transformations with Proeutectoid Materials
CO = 1.13 wt% C T(°C) T(°C) 900 1600 d A L 800 1400 A TE (727°C) g + 1200 g +L L+Fe3C 700 A C (austenite) P 1000 + P a g +Fe3C 600 A 800
727°C (cementite) C T a 3
500 600 +Fe3C Fe 2 3 4
1 10 10 10 10 400 0.76 0 0.022 1 2 3 4 5 6 6.7 time (s) (Fe) 1.13 Co, wt%C Adapted from Fig. 10.16, Adapted from Fig. 9.24, Callister 7e. Callister 7e.
Hypereutectoid composition – proeutectoid cementite
Chapter 10 -26 Hypereutectoid Steel T(°C) 1600 d 1400 L (Fe-C System) g g g g+L 1200 1148°C L+Fe C g g (austenite) 3 g g 1000 g g +Fe C Adapted from Figs. 9.24 g 3 and 9.32,Callister 7e. Fe C 3 r s (Fig. 9.24 adapted from g g 800 Binary Alloy Phase Diagrams, 2nd ed., Vol. g g (cementite) C a R S 3 1, T.B. Massalski (Ed.-in- 600 Chief), ASM International, wFe C =r/(r+s) a +Fe C 3 3 Fe Materials Park, OH, wg =(1-w Fe C) 3 400 1990.) 0 1 Co 2 3 4 5 6 6.7 (Fe) C , wt%C
pearlite 0.76 o w pearlite = wg wa =S/(R+S) Hypereutectoid w =(1-w a) 60 mm Fe3C steel
pearlite proeutectoid Fe3C Adapted from Fig. 9.33,Callister 7e. Chapter 10 -27 Non-Equilibrium Transformation Products: Fe-C • Bainite: --a lathes (strips) with long rods of Fe3C --diffusion controlled. Fe3C • Isothermal Transf. Diagram (cementite) a (ferrite) 800 Austenite (stable) T(°C) A TE P 600 100% pearlite pearlite/bainite boundary 5 mm (Adapted from Fig. 10.17, Callister, 7e. (Fig. 100% bainite 10.17 from Metals Handbook, 8th ed., B 0 Vol. 8, Metallography, Structures, and Phase 400 A 215-540 C Diagrams, American Society for Metals, Materials Park, OH, 1973.)
200
10-1 10 103 105 time (s) Adapted from Fig. 10.18, Callister 7e. (Fig. 10.18 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and Cooling Chapter 10 -28 Transformation Diagrams, American Society for Metals, 1997, p. 28.) Spheroidite: Fe-C System
• Spheroidite: a --a grains with spherical Fe3C (ferrite) --diffusion dependent.
--heat bainite or pearlite for long times Fe3C --reduces interfacial area (driving force) (cementite)
For example: 700oC, 18-24h 60 mm (Adapted from Fig. 10.19, Callister, 7e. (Fig. 10.19 copyright United States Steel Corporation, 1971.)
Chapter 10 -29 Martensite: Fe-C System • Martensite: --g(FCC) to Martensite (BCT) (involves single atom jumps)
Fe atom x m
potential m sites x x
x x C atom sites 60 60 x (Adapted from Fig. 10.20, Callister, 7e. • Isothermal Transf. Diagram 800 Austenite (stable) Martensite needles Austenite T(°C) A TE P (Adapted from Fig. 10.21, Callister, 7e. 600 (Fig. 10.21 courtesy United States Steel Corporation.) Adapted from Fig. 10.22, B Callister 7e. 400 A • g to M transformation.. -- is rapid! Diffusionless transformation 0% -- % transf. depends on T only. 200 M + A 50% M + A 90% M + A -1 3 5 10 10 10 10 time (s) Chapter 10 -30 Martensite Formation
slow cooling g (FCC) a (BCC) + Fe3C quench tempering M (BCT)
M = martensite is body centered tetragonal (BCT)
Diffusionless transformation BCT if C > 0.15 wt% BCT few slip planes hard, brittle
Chapter 10 -31 Phase Transformations of Alloys
Effect of adding other elements Change transition temp.
Cr, Ni, Mo, Si, Mn
retard g a + Fe3C transformation
•Plain carbon steels •Alloy steels
Adapted from Fig. 10.23, Callister 7e.
Chapter 10 -32 Cooling Curve
plot temp vs. time
Isothermal heat treatment is not the most practical to conduct
Continuous cooling
Adapted from Fig. 10.25, Callister 7e.
Chapter 10 -33 Dynamic Phase Transformations
On the isothermal transformation diagram for 0.45 wt% C Fe-C alloy, sketch and label the time-temperature paths to produce the following microstructures: a) 42% proeutectoid ferrite and 58% coarse pearlite b) 50% fine pearlite and 50% bainite c) 100% martensite d) 50% martensite and 50% austenite
Chapter 10 -34 Example Problem for Co = 0.45 wt% a) 42% proeutectoid ferrite and 58% coarse pearlite
800 A + a first make ferrite A then pearlite T (°C) A + P 600 P B course pearlite A + B A higher T 400 50% M (start) M (50%) M (90%) 200
Adapted from Fig. 10.29, Callister 5e. 0 0.1 10 103 105 time (s) Chapter 10 -35 Example Problem for Co = 0.45 wt% b) 50% fine pearlite and 50% bainite
800 A + a first make pearlite A T (°C) then bainite A + P 600 P B A + B fine pearlite A 400 50% lower T M (start) M (50%) M (90%) 200
Adapted from Fig. 10.29, Callister 5e. 0 0.1 10 103 105 time (s) Chapter 10 -36 Example Problem for Co = 0.45 wt% c) 100 % martensite – quench = rapid cool d) 50 % martensite 800 A + a and 50 % A austenite T (°C) A + P 600 P B A + B A 400 50% M (start) M (50%) d) M (90%) 200
Adapted from c) Fig. 10.29, Callister 5e. 0 0.1 10 103 105 time (s) Chapter 10 -37 Mechanical Prop: Fe-C System (1)
• Effect of wt% C Pearlite (med) Pearlite (med) Cementite ferrite (soft) (hard) Adapted from Fig. 9.30,Callister Co < 0.76 wt% C Co > 0.76 wt% C Adapted from Fig. 9.33,Callister 7e. 7e. (Fig. 9.30 courtesy Republic (Fig. 9.33 copyright 1971 by United Steel Corporation.) Hypoeutectoid Hypereutectoid States Steel Corporation.) Hypo Hyper Hypo Hyper TS(MPa) 1100 %EL 80
YS(MPa) lb) 100 - Adapted from Fig. 10.29, Callister 7e. 900 hardness (Fig. 10.29 based on 40 data from Metals 700 Handbook: Heat 50 Treating, Vol. 4, 9th ed., V. Masseria 500 (Managing Ed.), 0 American Society for 300 Metals, 1981, p. 9.)
0 ft energy(Izod, Impact 0 0.5 1 0 0.5 1
0.76 wt% C 0.76 wt% C • More wt% C: TS and YS increase, %EL decreases.
Chapter 10 -38 Mechanical Prop: Fe-C System (2)
• Fine vs coarse pearlite vs spheroidite
Hypo Hyper 90 Hypo Hyper 320
fine spheroidite pearlite 60 240 coarse pearlite spheroidite 160 30 coarse Ductility(%AR) pearlite
Brinellhardness fine 80 pearlite 0 0 0.5 1 0.5 1 wt%C 0 wt%C Adapted from Fig. 10.30, Callister 7e. • Hardness: fine > coarse > spheroidite (Fig. 10.30 based on data from Metals Handbook: Heat Treating, Vol. 4, 9th • %RA: fine < coarse < spheroidite ed., V. Masseria (Managing Ed.), American Society for Metals, 1981, pp. 9 and 17.)
Chapter 10 -39 Mechanical Prop: Fe-C System (3)
• Fine Pearlite vs Martensite:
Hypo Hyper
600 martensite Adapted from Fig. 10.32, Callister 7e. (Fig. 10.32 adapted 400 from Edgar C. Bain, Functions of the Alloying Elements in Steel, American Society for Metals,
Brinellhardness 1939, p. 36; and R.A. Grange, 200 C.R. Hribal, and L.F. Porter, fine pearlite Metall. Trans. A, Vol. 8A, p. 1776.) 0 0.5 1 0 wt% C • Hardness: fine pearlite << martensite. Martensite: not related to microstructure, rather to the effectiveness of the interstitial carbon atoms in hindering dislocation motion , and the relatively few slip systems for BCT structure. Chapter 10 -40 Tempering Martensite • reduces brittleness of martensite, • reduces internal stress caused by quenching. TS(MPa) YS(MPa) 1800
1600 TS Adapted from Adapted from Fig. 10.34, 1400 YS Fig. 10.33,
Callister 7e. m Callister 7e. m (Fig. 10.34 (Fig. 10.33
1200 9 adapted from 60 copyright by Fig. furnished United States 1000 50 courtesy of %RA %RA Steel Republic Steel 40 Corporation, Corporation.) 1971.) 800 30 200 400 600 Tempering T(°C)
• produces extremely small Fe3C particles surrounded by a. • decreases TS, YS but increases %RA Chapter 10 -41 Summary: Processing Options
Adapted from Austenite (g) Fig. 10.36, Callister 7e. slow moderate rapid cool cool quench
Pearlite Bainite Martensite
(a + Fe3C layers + a (a + Fe3C plates/needles) (BCT phase proeutectoid phase) diffusionless transformation) Martensite reheat T Martensite bainite Tempered fine pearlite Martensite
(a + very fine Ductility Strength coarse pearlite spheroidite Fe3C particles) General Trends Chapter 10 -42