Chapter 10: Phase Transformations ISSUES TO ADDRESS... • Transforming one phase into another takes time. Fe g (Austenite) Eutectoid transformation C FCC Fe3C (cementite) a (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?

Phase transformations are divided into three classifications: simple diffusion-dependent transformations in which there is no change in either the number or composition of the phases present.( Ex. Solidification of a pure metal, allotropic transformations, recrystallization and grain growth) another type of diffusion-dependent transformation, there is some alteration in phase compositions and often in the number of phases present; the final microstructure ordinarily consists of two phases ( Ex. The eutectoid reaction) The third kind of transformation is diffusionless, wherein a metastable phase is produced.( Ex. martensitic transformation)

The progress of a phase transformation may be broken down into two distinct stages: nucleation: involve the appearance of very small particles, or nuclei of the new phase which are capable of growing. Favorable positions for the formation of these nuclei are imperfection sites, especially grain boundaries. growth : the nuclei increase in size; during this process, of course, some volume of the parent phase disappears. The transformation reaches completion if growth of these new phase particles is allowed to proceed until the equilibrium fraction is attained.

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) In Chapter 9 we looked at the equilibrium phase diagram . This indicated phase structure if we wait long enough. But due to slow diffusion may not reach equilibrium We need to consider time- kinetics - energy of phase boundaries may be high. – also nucleation Transformation rate How fast do the phase transformations occur? First need nuclei (seeds) to form for the rest of the material to crystallize Small supercooling  few nuclei - large crystals Large supercooling  rapid nucleation - many nuclei, small crystals

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

Homogeneous nucleation Related to Gibbs free energy G Free energy is a function of other thermodynamics parameters: internal energy of the system ( the enthalpy H) a measurements of the randomness or disorder of the atoms ( the entropy ) Transformation will occur spontaneously only when ∆G has a negative value

There are two contributions to the total free energy change that accompany a solidification transformation: Free energy difference between the solid and liquid phases(or the volume free energy ∆Cv : negative if the T is below the equilibrium solidification temperature; - the magnitude = ∆Gv x Volume of the spherical nucleus(4/3πr3 ) The second energy results from the formation of the solid-liquid phase boundary during the solidification transformation( or the surface free energy γ) which is positive - the magnitude = γ x The surface area of the nucleus(4πr2 ) The total free energy change ∆G = 4/3πr3 ∆Gv + 4πr2 γ A critical free energy ∆G* occurs at the critical radius and, consequently at the maximum of the curve. This ∆G* corresponds to an activation free energy, which is the free energy required for the formation of a stable nucleus. Equivalent, it may be considered an energy barrier to the nucleation process.

Homogeneous Nucleation & Energy Effects Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface) g = surface tension DGT = Total Free Energy = DGS + DGV Volume (Bulk) Free Energy – stabilizes the nuclei (releases energy) r* = critical radius of nucleus: nuclei < r* shrink; nuclei>r* grow (to reduce energy)

Since r* and ∆G* appear at the maximum on the free energy-versus-radius curve, we can find r* and ∆G* by derivation equ. This volume free energy change ∆Gv is the driving force for the solidification transformation, and its magnitude is a function of temperature Tm, the value of ∆Gv is zero, and with diminishing temperature its value becomes increasingly more negative.

Solidification Note: HS = strong function of T HS = latent heat of solidification Tm = melting temperature g = surface free energy DT = Tm - T = supercooling r* = critical radius Note: HS = strong function of T  = weak function of T r * decreases as T increases ∆G* decreases as T increases For typical T r* ca. 100Å

There are two important parameters ( temperature-dependent) influence nucleation: The number of stable nuclei n* ( having radii greater than r* ) the clustering of atoms by short – range diffusion during the formation of nuclei Qd – activation energy for diffusion ( temp. independent) K2 temp.independent constant

Nucleation rate - it has units of nuclei per unit volume per second Nucleation rate expression for homogeneous nucleation K3 – the number of atoms on a nucleus surface Comments: This method may be applied to any shape with the same final result May be utilized for types of transformations other than solidification ( ex. Solid-vapor, solid-solid) For solid – solid transformation, there may be volume changes attendant to the formation of new phases, consequently will affect the magnitudes of r* and ∆G*

Tm νd N temperature n* Supercooling (undercooling): when during the cooling of liquid an appreciable nucleation rate ( i.e., solidification) will begin only after the temperature has been lowered to below the equilibrium solidification ( or melting) temperature Tm . The degree of supercooling may be significant. Superheating: Heating to above a phase transition temperature without the occurrence of the transformation.

Heterogeneous nucleation It is a nucleation which occurs at surfaces and interfaces( which is easier than other sites, because of the activation energy ( energy barrier) for nucleation is lowered when nuclei form on preexisting surfaces or interfaces, since the surface free energy is reduced. liquid θ solid S(θ) is a function only of θ ( the shape of nucleus), which will have a numerical value between zero and unity.

r* ∆G r Heterogeneous nucleation occurs more readily

Tm temperature Nhet Nhom Nucleation rate

Growth The growth step in a phase transformation begins once an embryo has exceeded the critical size, r* and becomes a stable nucleus. The nuclei increase in size; during this process, of course, some volume of the parent phase disappears. The transformation reaches completion if growth of these new phase particles is allowed to proceed until the equilibrium fraction is attained The growth rate G is determined by the rate of diffusion, and its temperature dependence is the same for the diffusion coefficient

Overall transformation rate Tm Growth rate, G temperature Overall transformation rate Nucleation rate, N Rate Overall transformation rate is equal to some product of N and G. the size of product phase is particles will depend on transformation temperature.

Rate of Phase Transformations Kinetics - measure approach to equilibrium vs. time Hold temperature constant & measure conversion vs. time How is conversion measured? X-ray diffraction – have to do many samples electrical conductivity – follow one sample sound waves – one sample

Rate of Phase Transformation All out of material - done Fixed T Fraction transformed, y 0.5 maximum rate reached – now amount unconverted decreases so rate slows rate increases as surface area increases & nuclei grow t0.5 log t Logarithm of heating time, t S.A. = surface area Avrami rate equation => y = 1- exp (-kt n) k & n fit for specific sample(time independent constant fraction transformed time The rate of transformation r is taken as the reciprocal of time required to Proceed halfway completation By convention r = 1 / t0.5

Rate of Phase Transformations 135C 119C 113C 102C 88C 43C 1 10 102 104 In general, rate increases as T  r = 1/t0.5 = A e -Q/RT R = gas constant T = temperature (K) A = preexponential factor Q = activation energy Arrhenius expression r often small: equilibrium not possible!

Eutectoid Transformation Rate • Growth of pearlite from austenite: g a pearlite growth direction Austenite (g) grain boundary cementite (Fe3C) Ferrite (a) Diffusive flow of C needed a g • Recrystallization rate increases with DT. 675°C (DT smaller) 50 y (% pearlite) 600°C (DT larger) 650°C 100 Course pearlite  formed at higher T - softer Fine pearlite  formed at low T - harder

Nucleation and Growth • Reaction rate is a result of nucleation and growth of crystals. % Pearlite 50 100 Nucleation regime Growth log (time) t 0.5 Nucleation rate increases with T Growth rate increases with T • Examples: T just below TE Nucleation rate low Growth rate high g pearlite colony T moderately below TE g Nucleation rate med . Growth rate med. Nucleation rate high T way below TE g Growth rate low

Transformations & Undercooling • Eutectoid transf. (Fe-C System): g Þ 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!) Fe3C (cementite) 1600 1400 1200 1000 800 600 400 1 2 3 4 5 6 6.7 L g (austenite) +L +Fe3C a L+Fe3C d (Fe) Co , wt%C 1148°C T(°C) ferrite 727°C Eutectoid: Equil. Cooling: Ttransf. = 727ºC DT Undercooling by DTtransf. < 727C 0.76 0.022

Microstructure and property changes in Iron – Carbon Alloys Pearlite Bainite Spheroidite Martensite

Isothermal Transformation Diagrams Consider again the iron–iron carbide eutectoid reaction which is fundamental to the development of microstructure in steel alloys. Upon cooling, austenite, having an intermediate carbon concentration, transforms to a ferrite phase, having a much lower carbon content, and also cementite, with a much higher carbon concentration. Pearlite is one microstructural product of this transformation Temperature and time play an important role in the rate of the austenite-to- pearlite transformation

Isothermal Transformation Diagrams • Fe-C system, Co = 0.76 wt% C • Transformation at T = 675°C. 100 T = 675°C Transformation end y, % transformed 50 Transformation beginning 2 4 1 10 10 time (s) 400 500 600 700 1 10 2 3 4 5 0%pearlite 100% 50% Austenite (stable) TE (727C) Austenite (unstable) Pearlite T(°C) time (s) isothermal transformation at 675°C

Several constraints are imposed on using diagrams like Figure before: This particular plot is valid only for an iron–carbon alloy of eutectoid composition; for other compositions, the curves will have different configurations These plots are accurate only for transformations in which the temperature of the alloy is held constant throughout the duration of the reaction such as Figure are referred to as isothermal transformation diagrams, or sometimes as time–temperature–transformation (or T–T–T) plots.

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. 400 500 600 700 0%pearlite 100% 50% Austenite (stable) TE (727C) Austenite (unstable) Pearlite T(°C) 1 10 2 3 4 5 time (s) A C D 625 B An actual isothermal heat treatment curve (ABCD) on the TTT diagram g g

Coarse pearlite: This microstructure has relatively thick layers of both the -ferrite and Fe3C –phases at temperatures just below the eutectoid Fine pearlite: The thin-layered structure produced in the vicinity of 540C because of decreasing temperature, and so the decrease of carbon diffusion rate

Transformations with Proeutectoid Materials CO = 1.13 wt% C TE (727°C) T(°C) time (s) A + C P 1 10 102 103 104 500 700 900 600 800 Fe3C (cementite) 1600 1400 1200 1000 800 600 400 1 2 3 4 5 6 6.7 L g (austenite) +L +Fe3C a L+Fe3C d (Fe) Co , wt%C T(°C) 727°C DT 0.76 0.022 1.13 Hypereutectoid composition – proeutectoid cementite

Non-Equilibrium Transformation Products: Fe-C • Bainite: --a lathes (strips) with long rods of Fe3C --diffusion controlled. • Isothermal Transf. Diagram Fe3C (cementite) a (ferrite) 10 3 5 time (s) -1 400 600 800 T(°C) Austenite (stable) 200 P B TE 0% 100% 50% pearlite/bainite boundary A 100% pearlite 100% bainite 5 mm It occurs at temperatures below those at which pearlite forms; begin-, end-, and half-reaction curves are just extensions of those for the pearlitic transformation Pearlite forms above the nose—that is, over the temperature range of about 540 to 727. At temperatures between about 215 and 540C Bainite is the transformation product.

Spheroidite: Fe-C System Spheroidite is formed when a steel alloy having either pearlitic or bainitic microstructures is heated to, and left at, a temperature below the eutectoid for a sufficiently long period of time—for example, at about 700C (1300F) for between 18 and 24 h 60 m a (ferrite) (cementite) Fe3C The Fe3C phase appears as spherelike particles embedded in a continuous α phase matrix. • Spheroidite: --a grains with spherical Fe3C --diffusion dependent. --heat bainite or pearlite for long times --reduces interfacial area (driving force)

Martensite: Fe-C System --g(FCC) to Martensite (BCT) Martensite needles Austenite 60 m x potential C atom sites Fe atom sites (involves single atom jumps) (Adapted from Fig. 10.20, Callister, 7e. • Isothermal Transf. Diagram 10 3 5 time (s) -1 400 600 800 T(°C) Austenite (stable) 200 P B TE 0% 100% 50% A M + A 90% • g to M transformation.. -- is rapid!(quenching process) -- % transf. depends on T only -- time independent

Martensite Formation  (FCC)  (BCC) + Fe3C Is formed when austenitized iron–carbon alloys are rapidly cooled (or quenched) to a relatively low temperature (in the vicinity of the ambient)  (FCC)  (BCC) + Fe3C slow cooling quench M (BCT) tempering M = martensite is body centered tetragonal (BCT) Diffusionless transformation BCT if C > 0.15 wt% BCT  few slip planes  hard, brittle Martensite is a nonequilibrium single-phase structure that results from a diffusionless transformation of austenite(rapid cooling prevent carbon diffusion).

Phase Transformations of Alloys Effect of adding other elements Change transition temp. changes in the positions and shapes of the curves in the isothermal transformation diagrams. Cr, Ni, Mo, Si, Mn retard    + Fe3C transformation

CONTINUOUS COOLING TRANSFORMATION DIAGRAMS An isothermal transformation diagram is valid only for conditions of constant temperature, which diagram must be modified for transformations that occur as the temperature is constantly changing. For continuous cooling, the time required for a reaction to begin and end is delayed. A plot containing such modified beginning and ending reaction curves is termed a continuous cooling transformation (CCT) diagram.

Cooling Curve plot temp vs. time Actual processes involves cooling – not isothermal Can’t cool at infinite speed

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: 42% proeutectoid ferrite and 58% coarse pearlite 50% fine pearlite and 50% bainite 100% martensite 50% martensite and 50% austenite

Example Problem for Co = 0.45 wt% 42% proeutectoid ferrite and 58% coarse pearlite first make ferrite then pearlite coarse pearlite  higher T A + B A + P A + a A B P 50% 200 400 600 800 0.1 10 103 105 time (s) M (start) M (50%) M (90%) T (°C)

Example Problem for Co = 0.45 wt% 50% fine pearlite and 50% bainite first make pearlite then bainite fine pearlite  lower T A + B A + P A + a A B P 50% 200 400 600 800 0.1 10 103 105 time (s) M (start) M (50%) M (90%) T (°C)

Example Problem for Co = 0.45 wt% 100 % martensite – quench = rapid cool 50 % martensite and 50 % austenite A + B A + P A + a A B P 50% 200 400 600 800 0.1 10 103 105 time (s) M (start) M (50%) M (90%) c) T (°C) d)

Mechanical Prop: Fe-C System Pearlite: -- Cementite is much harder but more brittle than ferrite -- increasing the fraction of Fe3C in a steel alloy while holding other microstructural elements constant will result in a harder and stronger material -- Fine pearlite is harder and stronger than coarse pearlit because of different in the layer thickness of each of the ferrite and cementite phases -- Coarse pearlite is more ductile than fine pearlite, because of the greater restriction to plastic deformation of the fine pearlite

Spheroidite: -- Alloys containing pearlitic microstructures have greater strength and hardness than do those with spheroidite. This behavior is explained in terms of reinforcement at, and impedance to, dislocation motion across the ferrite–cementite boundaries as discussed above. There is less boundary area per unit volume in spheroidite, and consequently plastic deformation is not nearly as constrained, which gives rise to a relatively soft and weak material. In fact, of all steel alloys, those that are softest and weakest have a spheroidite microstructure -- spheroidized steels are extremely ductile, much more than either fine or coarse pearlite .In addition, they are notably tough because any crack can encounter only a very small fraction of the brittle cementite particles as it propagates through the ductile ferrite matrix.

Bainite: -- Because bainitic steels have a finer structure (i.e., smaller -ferrite and Fe3C particles), they are generally stronger and harder than pearlitic ones; yet they exhibit a desirable combination of strength and ductility. Martinsite: -- Martensite is the hardest and strongest and, the most brittle; it has, in fact, negligible ductility. Its hardness is dependent on the carbon content, up to about 0.6 wt%. these properties are attributed to the effectiveness of the interstitial carbon atoms in hindering dislocation motion (as a solid-solution effect) and to the relatively few slip systems (along which dislocations move) for the BCT structure.

Mechanical Prop: Fe-C System (1) Pearlite (med) • Effect of wt% C C ementite (hard) Pearlite (med) ferrite (soft) Co < 0.76 wt% C Co > 0.76 wt% C Hypoeutectoid Hypereutectoid

• More wt% C(or equivalent Fe3C): TS and YS increase , %EL decreases. 300 500 700 900 1100 YS(MPa) TS(MPa) wt% C 0.5 1 hardness 0.76 Hypo Hyper wt% C 0.5 1 50 100 %EL Impact energy (Izod, ft-lb) 40 80 0.76 Hypo Hyper • More wt% C(or equivalent Fe3C): TS and YS increase , %EL decreases.

Mechanical Prop: Fe-C System (2) • Fine vs coarse pearlite vs spheroidite 80 160 240 320 wt%C 0.5 1 Brinell hardness fine pearlite coarse spheroidite Hypo Hyper 30 60 90 wt%C Ductility (%AR) fine pearlite coarse spheroidite Hypo Hyper 0.5 1 • Hardness: fine > coarse > spheroidite • %RA: fine < coarse < spheroidite

Mechanical Prop: Fe-C System (3) • Fine Pearlite vs Martensite: 200 wt% C 0.5 1 400 600 Brinell hardness martensite fine pearlite Hypo Hyper • Hardness: fine pearlite << martensite.

Tempering Martensite • • • reduces brittleness of martensite, enhanced ductility and tough. • reduces internal stress caused by quenching. YS(MPa) TS(MPa) 800 1000 1200 1400 1600 1800 30 40 50 60 200 400 600 Tempering T (°C) %RA TS YS 9 mm produces extremely small Fe3C particles surrounded by a. • • decreases TS, YS but increases %RA

Tempering is accomplished by heating a martensitic steel to a temperature below the eutectoid for a specified time period. Normally, tempering is carried out at temperatures between 250 and 650C ; internal stresses, however, may be relieved at temperatures as low as 200C.This tempering heat treatment allows, by diffusional processes, the formation of tempered martensite, according to the reaction The size of the cementite particles influences the mechanical behavior of tempered martensite; increasing the particle size decreases the ferrite–cementite phase boundary area and, consequently, results in a softer and weaker material yet one that is tougher and more ductile Heat treatment variables are temperature and time, and most treatments are constant-temperature processes. Since carbon diffusion is involved in the martensite-tempered martensite transformation, increasing the temperature will accelerate diffusion, the rate of cementite particle growth, and, subsequently, the rate of softening.

Summary: Processing Options Austenite (g) Bainite (a + Fe3C plates/needles) Pearlite (a + Fe3C layers + a proeutectoid phase) Martensite (BCT phase diffusionless transformation) Tempered (a + very fine Fe3C particles) slow cool moderate rapid quench reheat Strength Ductility T Martensite bainite fine pearlite coarse pearlite spheroidite General Trends