Chapter 10: Phase Transformations
Chapter 10:Phase TransformationsISSUES TO ADDRESS. Transforming one phase into another takes time.Feg(Austenite)CFCCFe C3Eutectoidtransformation (cementite) a(ferrite)(BCC) How does the rate of transformation depend ontime and T? How can we slow down the transformation so thatwe can engineering non-equilibrium structures? Are the mechanical properties of non-equilibriumstructures better?Chapter 10 - 1
Phase transformation Takes time (transformation rates: kinetics).Involves movement/rearrangement of atoms.Usually involves changes in microstructure1.“Simple” diffusion-dependent transformation: no change in numberof compositions of phases present (e.g. solidification of pureelemental metals, allotropic transformation, recrystallization,grain growth).2.Diffusion-dependent transformation: transformation with alterationin phase composition and, often, with changes in number ofphases present (e.g. eutectoid reaction).3.Diffusionless transformation: e.g. rapid T quenching to “trap”metastable phases.Chapter 10 - 2
ºTR recrystallizationtemperatureTRAdapted from Fig.7.22, Callister 7e.The influence ofannealing T on thetensile strength andductility of a brassalloy.ºChapter 10 - 3
Iron-Carbon Phase DiagramEutectoid cooling:coolg (0.76 wt% C)T( C)a (0.022 wt% C) Fe3C (6.7 wt% C)heat1600d1200g Lg(austenite)g gg g1000a800Sg Fe3C727 C TeutectoidR4000(Fe)S10.76L Fe3CRBC eutectoid600A1148 C23a Fe3C456Fe3C (cementite)L14006.74.30Co, wt% CFe3C (cementite-hard)a (ferrite-soft)Adapted from Fig. 9.24,Callister 7e.Chapter 10 - 4
Phase TransformationsNucleation– nuclei (seeds) act as template to grow crystals– for nucleus to form rate of addition of atoms tonucleus must be faster than rate of loss– once nucleated, grow until reach equilibriumDriving force to nucleate increases as we increase T– supercooling (eutectic, eutectoid)– superheating (peritectic)Small supercooling few nuclei - large crystalsLarge supercooling rapid nucleation - many nuclei,small crystalsChapter 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 alreadypresent Could be wall of mold or impurities in the liquidphase– allows solidification with only 0.1-10ºCsupercoolingPhase 1 (e.g. liquid)Nucleation of2ndphaseChapter 10 - 6Growth
Homogeneous NucleationThermodynamic parameters: Free energy G (or Gibbs free energy) Enthalpy H: internal energy of the system and the product of itsvolume multiplied by the pressure Entropy S: randomness or disorder of the atoms or moleculesΔG is important---a phase transformation will occurspontaneously only when ΔG has a negative value.ΔG ΔH - TΔSChapter 10 - 7
Homogeneous NucleationChapter 10 - 8
Homogeneous Nucleation & Energy EffectsSurface Free Energy- destabilizesthe nuclei (it takes energy to makean interface) GS 4 r 2 gActivation Free Energyg surface energy GT Total Free Energy GS GVVolume (Bulk) Free Energy –stabilizes the nuclei (releases energy)4 GV r 3 G 3 G volume free energyunit volumer* 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 reactionsCritical nucleus size (rc) and the activation energy ( G*)4 3 G r Gv 4 r 2g3Take the derivative and set equal to zero to find max.d ( G) 42 ( Gv )(3r ) 4 g (2r ) 0dr32grc GvSubstitution in to overall G equation316 g G * 3( Gv ) 2Chapter 10 - 10The volume free energy change is the driving force for the solidification transformation
Kinetics of solid state reactionsIn terms of latent heat of fusion Hf (i.e. energy release upon solidification): Gv H f (Tm T )Tells us how Gv changes with ith this definition, we then have:2grc H fT1 T2 Tm Tm T 16 g Tm G 2 3 H f Tm T 32*As T decreases both rcand G* become smaller* G* Number of stable nuclei: n exp kT Chapter 10 - 11LIQUID INSTABILITY at LOWER TEMPERTURES
Solidification 2gTmr* HS Tr* critical radiusg surface free energyTm melting temperature HS latent heat of solidification T Tm - T supercoolingNote: HS strong function of Tg weak function of T r*decreases as T increasesFor typical Tr* ca. 100ÅChapter 10 - 12
Kinetics of solid state reactionsWe 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 Q D Do exp d 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 reactionsCombining liquid instability and diffusion effects together:Rate of Nucleation (units: nuclei per unit volume per second)* G* n exp kT Liquid instability Qd vd exp kT DiffusionContribution fromliquid instabilityNucleation rate G * dN Qd Kn * vd K ' exp exp dtkTkT Contribution fromdiffusionNet rateTmChapter 10 - 14T
Example problem: critical radius andactivation energy for nucleationA) If pure liquid gold is cooled to 230oC below its melting point,calculate the critical radius and the activation energy. Values forthe latent heat of fusion and surface free energy are -1.16x109J/m3and 0.132J/m2, respectively.rc 2g H f Tm Tm T 1.32nm16 g Tm G 2 3 H f Tm T 32*9.64x10-19JB) Calculate the number of atoms per nucleus of this critical size. Au isFCC with a 0.413nm.4 r *3critical nucleus volume 3# unit cells/particle 1373unit cell volumea4 atoms/unit cell 548 atoms/critical nucleusChapter 10 - 15
Rate of Phase TransformationsKinetics – time dependence of nucleation,growth and transformation rates. Hold temperature constant & measuretransformation vs. timeHow is transformation measured? microscopic examinationX-ray diffraction – have to do many sampleselectrical conductivity – follow one samplesound waves – one sampleChapter 10 - 16
Fraction transformed, yRate of Phase TransformationAll out of material - doneFixed T0.5maximum rate reached – now amountunconverted decreases so rate slowsrate increases as surface area increasest0.5 & nuclei growlog tAvrami rate equation y 1- exp (-ktn)fractiontransformedAdapted fromFig. 10.10,Callister 7e.time– k & n fit for specific sampleBy conventionr 1 / t0.5Chapter 10 - 17
CuRate of Phase Transformations135 C 119 C110113 C 102 C88 C10243 CAdapted from Fig.10.11, Callister 7e.(Fig. 10.11 adaptedfrom B.F. Decker andD. Harker,"Recrystallization inRolled Copper", TransAIME, 188, 1950, p.888.)104 In general, rate increases as T r 1/t0.5 A e -Q/RT––––R gas constantT temperature (K)A preexponential factorQ activation energyArrheniusexpression r often small: equilibrium not possible!Chapter 10 - 18
Eutectoid cooling:coolg (0.76 wt% C)heata (0.022 wt% C) Fe3C (6.7 wt% C)Chapter 10 - 19
Eutectoid Transformation Rate Growth of pearlite from austenite:Adapted fromFig. 9.15,Callister 7e.aag aaaa Recrystallizationrate increaseswith T.gcementite (Fe3C)Ferrite (a)agapearlitegrowthdirectionga100y (% pearlite)Austenite (g)grainboundaryDiffusive flowof C needed600 C( T larger)50650 C675 C( T smaller)Adapted fromFig. 10.12,Callister 7e.0Course pearlite formed at higher T - softerFine pearlite formed at low T - harderChapter 10 - 20
Nucleation and Growth Reaction rate is a result of nucleation and growthof crystals.100% PearliteNucleation rate increases with TGrowthregime50 NucleationGrowth rate increases with Tregimet 0.50log (time)Adapted fromFig. 10.10, Callister 7e. Examples:gpearlitecolonyT just below TENucleation rate lowGrowth rate highgT moderately below TENucleation rate med .Growth rate med.gT way below TENucleation rate highGrowth rate lowChapter 10 - 21
Transformations & Undercoolingg a Fe3C Eutectoid transf. (Fe-C System): Can make it occur at:0.76 wt% C6.7 wt% C0.022 wt% C.727ºC (cool it slowly).below 727ºC (“undercool” it!)T( C)1600dg Lg1200(austenite)1000g Fe3CEutectoid:Equil. Cooling: Ttransf. 727ºC800727 C4000(Fe) Ta Fe3CUndercooling by Ttransf. 727 C0.766000.022aferriteL Fe3C1148 C123456Fe3C (cementite)L1400Adapted from Fig.9.24,Callister 7e. (Fig. 9.24adapted from Binary AlloyPhase Diagrams, 2nd ed.,Vol. 1, T.B. Massalski (Ed.in-Chief), ASM International,Materials Park, OH, 1990.)6.7Co , wt%CChapter 10 - 22
Isothermal Transformation DiagramsT-T-T plotsy,% transformed Fe-C system, Co 0.76 wt% C Transformation at T 675 C. T: hold constant100T 675 C50010 21T( C)Austenite (stable)10 4time (s)TE (727 C)700Austenite(unstable)600Pearliteisothermal transformation at 675 C50040011010 2 10 3 10 4 10 5Only for Fe-C alloy ofeutectoid compositionAdapted from Fig. 10.13,Callister 7e.(Fig. 10.13 adapted from H. Boyer (Ed.)Atlas of Isothermal Transformation andCooling Transformation Diagrams,American Society for Metals, 1977, p.369.)time (s)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) A700Austenite (stable)Austenite(unstable)CBD600gg500TE (727 C)PearlitegggAdapted from Fig.10.14,Callister 7e.(Fig. 10.14 adapted fromH. Boyer (Ed.) Atlas ofIsothermal Transformationand CoolingTransformation Diagrams,American Society forMetals, 1997, p. 28.)g40011010 210 310 410 5time (s)Chapter 10 - 24
PearliteCoarse (quenched to higher T)Fine (quenched to lower T)Chapter 10 - 25
Transformations withProeutectoid MaterialsCO 1.13 wt% CT( C)T( C)900dA 1200CA PaPL Fe3C(austenite)1000g Fe3C8006005001g Lg10102103time (s)Adapted from Fig. 10.16,Callister 7e.104 T4000(Fe)0.76600ATE (727 C)A1.13700L14000.0228001727 Ca Fe3C2345Adapted from Fig. 9.24,Callister 7e.6Fe3C (cementite)16006.7Co , wt%CHypereutectoid composition – proeutectoid cementiteChapter 10 - 26
Hypereutectoid SteelT( C)1600dLFe3Cggg Lg1200(austenite)gg1000g gg gr800w Fe3C r/(r s)w g (1-w Fe3C )a R6004000(Fe)pearliteL Fe3C1148 Cg Fe3C0.76gggg(Fe-CSystem)sS1 Cow pearlite w gw a S/(R S)w Fe3C (1-w a )a Fe3C23456Fe3C (cementite)1400Adapted from Figs. 9.24and 9.32,Callister 7e.(Fig. 9.24 adapted fromBinary Alloy PhaseDiagrams, 2nd ed., Vol.1, T.B. Massalski (Ed.-inChief), ASM International,Materials Park, OH,1990.)6.7Co , wt%C60 mmHypereutectoidsteelpearliteproeutectoid Fe3CAdapted from Fig. 9.33,Callister 7e.Chapter 10 - 27
Non-Equilibrium TransformationProducts: Fe-C Bainite:--a lathes (strips) with longrods of Fe3C--diffusion controlled. Isothermal Transf. Diagram800Austenite (stable)T( C)Aa (ferrite)TEP6005 mm100% pearlitepearlite/bainite boundary100% bainite400Fe3C(cementite)B215-5400CA(Adapted from Fig. 10.17, Callister, 7e. (Fig.10.17 from Metals Handbook, 8th ed.,Vol. 8, Metallography, Structures, and PhaseDiagrams, American Society for Metals,Materials Park, OH, 1973.)20010-110103105time (s)Adapted from Fig. 10.18, Callister 7e.(Fig. 10.18 adapted from H. Boyer (Ed.) Atlas of Isothermal Transformation and CoolingTransformation Diagrams, American Society for Metals, 1997, p. 28.)Chapter 10 - 28
Spheroidite: Fe-C System Spheroidite:a(ferrite)--a grains with spherical Fe3C--diffusion dependent.--heat bainite or pearlite for long timesFe3C--reduces interfacial area (driving force) (cementite)For example: 700oC, 18-24h60 mm(Adapted from Fig. 10.19, Callister, 7e.(Fig. 10.19 copyright United StatesSteel Corporation, 1971.)Chapter 10 - 29
Martensite: Fe-C System Martensite:--g(FCC) to Martensite (BCT)Fe atomsitesxxxxx60 mm(involves single atom jumps)potentialC atom sitesx(Adapted from Fig.10.20, Callister, 7e. Isothermal Transf. Diagram800Austenite (stable)T( C)A40010-1(Adapted from Fig. 10.21, Callister, 7e.(Fig. 10.21 courtesy United StatesSteel Corporation.) g to M transformation.BA200TEP600Adapted fromFig. 10.22,Callister 7e.Martensite needlesAustenite0%50%90%M AM AM A10103105-- is rapid! Diffusionless transformation-- % transf. depends on T only.time (s)Chapter 10 - 30
Martensite Formationg (FCC)slow coolinga (BCC) Fe3CquenchM (BCT)temperingM martensite is body centered tetragonal (BCT)Diffusionless transformationBCT few slip planesBCT if C 0.15 wt% hard, brittleChapter 10 - 31
Phase Transformations of AlloysEffect of adding other elementsChange transition temp.Cr, Ni, Mo, Si, Mnretard g a Fe3Ctransformation Plain carbon steels Alloy steelsAdapted from Fig. 10.23, Callister 7e.Chapter 10 - 32
Cooling Curveplot temp vs. timeIsothermal heat treatment isnot the most practical toconductContinuous coolingAdapted fromFig. 10.25,Callister 7e.Chapter 10 - 33
Dynamic Phase TransformationsOn the isothermal transformation diagram for0.45 wt% C Fe-C alloy, sketch and label thetime-temperature paths to produce thefollowing microstructures:a) 42% proeutectoid ferrite and 58% coarsepearliteb) 50% fine pearlite and 50% bainitec) 100% martensited) 50% martensite and 50% austeniteChapter 10 - 34
Example Problem for Co 0.45 wt%a) 42% proeutectoid ferrite and 58% coarse pearlitefirst make ferrite 800then pearlite T ( C)APB600course pearlite higher TA aA PA BA40050%M (start)M (50%)M (90%)200Adapted fromFig. 10.29,Callister 5e.00.110103time (s)105Chapter 10 - 35
Example Problem for Co 0.45 wt%b) 50% fine pearlite and 50% bainite800first make pearliteT ( C)then bainiteAPB600fine pearlite lower TA aA PA BA40050%M (start)M (50%)M (90%)200Adapted fromFig. 10.29,Callister 5e.00.110103time (s)105Chapter 10 - 36
Example Problem for Co 0.45 wt%c) 100 % martensite – quench rapid coold) 50 % martensite800A aand 50 %AT ( C)austenitePB600A PA BA40050%M (start)M (50%)M (90%)d)200Adapted fromFig. 10.29,Callister 5e.c)00.110103time (s)105Chapter 10 - 37
Mechanical Prop: Fe-C System (1) Effect of wt% CAdapted from Fig. 9.30,Callister7e. (Fig. 9.30 courtesy RepublicSteel Corporation.)TS(MPa)1100YS(MPa)Co 0.76 wt% CHypoeutectoidHypoHyperCo 0.76 wt% C Adapted from Fig. 9.33,Callister 7e.9.33 copyright 1971 by UnitedHypereutectoid (Fig.States Steel 000.510Adapted from Fig.10.29, Callister 7e.(Fig. 10.29 based ondata from MetalsHandbook: HeatTreating, Vol. 4, 9thed., V. Masseria(Managing Ed.),American Society forMetals, 1981, p. 9.)0.7600.76300Impact energy (Izod, ft-lb)Pearlite (med)ferrite (soft)Pearlite (med)Cementite(hard)10.50wt% Cwt% C More wt% C: TS and YS increase, %EL decreases.Chapter 10 - 38
Mechanical Prop: Fe-C System (2) Fine vs coarse pearlite vs sepearlitespheroidite160800 Hardness: %RA:0.51wt%CDuctility (%AR)Brinell 3000fine coarse spheroiditefine coarse spheroidite0.51wt%CAdapted from Fig. 10.30, Callister 7e.(Fig. 10.30 based on data from MetalsHandbook: Heat Treating, Vol. 4, 9thed., 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:Brinell hardnessHypo600HypermartensiteAdapted from Fig. 10.32,Callister 7e. (Fig. 10.32 adaptedfrom Edgar C. Bain, Functions ofthe Alloying Elements in Steel,American Society for Metals,1939, p. 36; and R.A. Grange,C.R. Hribal, and L.F. Porter,Metall. Trans. A, Vol. 8A, p.1776.)400200fine pearlite000.51wt% C Hardness: fine pearlite martensite.Martensite: not related to microstructure, rather to the effectiveness ofthe interstitial carbon atoms in hindering dislocation motion , and therelatively 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)1800Adapted from1400Fig. 10.34,Callister 7e.(Fig. 10.341200adapted fromFig. furnished1000courtesy ofRepublic SteelCorporation.)800200TSYS6050%RA4030%RA4009 mm1600Adapted fromFig. 10.33,Callister 7e.(Fig. 10.33copyright byUnited StatesSteelCorporation,1971.)600Tempering T ( C) produces extremely small Fe3C particles surrounded by a. decreases TS, YS but increases %RAChapter 10 - 41
Summary: Processing OptionsAustenite (g)slowcoolmoderatecoolAdapted fromFig. 10.36,Callister 7e.rapidquenchBainiteMartensite(a Fe3C layers aproeutectoid phase)(a Fe3C plates/needles)(BCT phasediffusionlesstransformation)MartensiteT Martensitebainitefine pearlitecoarse pearlitespheroiditeGeneral nsite(a very fineFe3C particles)Chapter 10 - 42
Phase Transformations. Chapter 10 - 2 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 .
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
Phase Transformation in Metals Development of microstructure in both single- and two-phase alloys involves phase transformations-which involves the alteration in the number and character of the phases. Phase transformations take time and this allows the definition of transformation rate or kinetics. Phase transformations alter the microstructure and there can be three different classes of .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
Phase Transformations in Metals and Alloys ( This is the major reference for this course ) D.A.Porter, K.E. Easterling, and M.Y. Sharif CRC Press , Taylor & Francis Group Diffusion in solids Prof. Alok Paul , IISC Banglore NPTEL Web course Phase Transformations Prof. Anandh Subramaniam IIT Kanpur Phase Transformations & Heat Treatment Prof. M.P.Gururajan NPTEL web course Phase Transformations .
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
Phase transformations involve change in structure and (for multi-phase systems) composition rearrangement and redistribution of atoms via diffusion is required. The process of phase transformation involves: Nucleation of the new phase(s) - formation of stable small particles are often formed at grain Growth of the new phase(s) at the expense of the original phase(s). once nucleated, growth .
Phase Transformations in Metals 10.1 Introduction We may use time and temperature dependencies to modify some phase diagrams to develop phase transformation diagrams. It is important to know how to use these transformation diagrams in order design a heat treatment for some alloy that will yield the desired room-temperature mechanical properties. Inasmuch as most phase transformations do not .
Structural phase transformations in metallic grain boundaries Timofey Frolov1, David L. Olmsted1, Mark Asta1 & Yuri Mishin2 Structural transformations at interfaces are of profound fundamental interest as complex examples of phase transitions in low-dimensional systems. Despite decades of extensive research, no compelling evidence exists for structural transformations in high-angle grain .
