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Chapter 11: Phase Transformations

Chapter 11

Phase Transformations

Fe3C (cementite)- orthorhombicMartensite - BCT

Austenite - FCCFerrite - BCC1Phase TransformationsTransformation rateKinetics of Phase TransformationNucleation: homogeneous, heterogeneousFree Energy, GrowthIsothermal Transformations (TTT diagrams)Pearlite, Martensite, Spheroidite, BainiteContinuous CoolingMechanical BehaviorPrecipitation Hardening2In the study of phase transformations we will be dealing with the changes that can occur within a given system alloy that can exist as a mixture of one or more phasesA phase can be defined as a portion of the system whose properties and composition are homogeneous and which is physically distinct from other parts of the systemThe components of a system are the different elements or chemical compound which make up the systemPhase Transformations3

EquilibriumAny transformation that results in a decrease in Gibbs free energy is possible

4Phase TransformationsPhase transformations change in the number or character of phases.Simple diffusion-dependentNo change in # of phasesNo change in compositionExample: solidification of a pure metal, allotropic transformation, recrystallization, grain growthMore complicated diffusion-dependentChange in # of phasesChange in compositionExample: eutectoid reactionDiffusionlessExample: metastable phase - martensite5Phase TransformationsMost phase transformations begin with the formation of numerous small particles of the new phase that increase in size until the transformation is complete.Nucleation is the process whereby nuclei (seeds) act as templates for crystal growth. Homogeneous nucleation - nuclei form uniformly throughout the parent phase; requires considerable supercooling (typically 80-300C).Heterogeneous nucleation - form at structural inhomogeneities (container surfaces, impurities, grain boundaries, dislocations) in liquid phase much easier since stable nucleating surface is already present; requires slight supercooling (0.1-10C).6SupercoolingDuring the cooling of a liquid, solidification (nucleation) will begin only after the temperature has been lowered below the equilibrium solidification (or melting) temperature Tm. This phenomenon is termed supercooling (or undercooling.The driving force to nucleate increases as T increasesSmall supercooling slow nucleation rate - few nuclei - large crystalsLarge supercooling rapid nucleation rate - many nuclei - small crystals7

Nucleation of a spherical solid particle in a liquidc11f01LiquidThe change in free energy DG (a function of the internal energy and enthalpy of the system) must be negative for a transformation to occur.Assume that nuclei of the solid phase form in the interior of the liquid as atoms cluster together-similar to the packing in the solid phase. Also, each nucleus is spherical and has a radius r.Free energy changes as a result of: 1) the difference between the solid and liquid phases (volume free energy, DGV); and 2) the solid-liquid phase boundary (surface free energy, DGS). Transforming one phase into another takes time.DG = DGS + DGV Feg(Austenite)Eutectoid transformationCFCCFe3C(cementite)a (ferrite)+(BCC)8

r* = critical nucleus: for r < r* nuclei shrink; for r >r* nuclei grow (to reduce energy) Homogeneous Nucleation & Energy EffectsDGT = Total Free Energy = DGS + DGV Surface Free Energy- destabilizes the nuclei (it takes energy to make an interface)

g = surface tensionVolume (Bulk) Free Energy stabilizes the nuclei (releases energy)

9Effect of Temperature


Note: Hf and are weakly dependent on T r* decreases as T increasesFor typical T r* ~ 10 nmHf = latent heat of solidification (fusion)Tm = melting temperatureg = surface free energyDT = Tm - T = supercoolingr* = critical radius11Effect of Temperature

12GrowthIt begins once an embryo has exceeded the critical size r*nucleation will continue to occur simultaneously with growthThe growth process will cease in any region where particles of the new phase meetGrowth occurs by long-range atomic diffusiondiffusion through the parent phase, across a phase boundary, and then into the nucleus.

13growth rate


c11tf0115Computation of Critical Nucleus Radius and Activation Free Energy(a) For the solidification of pure gold, calculate the critical radius r*and the activation free energy G* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are -1.16 x109 J/m3 and 0.132 J/m2 , respectively. Use the super-cooling value found in Table 10.1.(b) Now calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.413 nm for solid gold at its melting temperature.16Transformations & Undercooling For transformation to occur, must cool to below 727C Eutectoid transformation (Fe-Fe3C system):ga+Fe3C0.76 wt% C0.022 wt% C6.7 wt% CFe3C (cementite)160014001200100080060040001234566.7Lg (austenite)g+Lg +Fe3Ca +Fe3CL+Fe3Cd(Fe)C, wt% C1148CT(C)aferrite727CEutectoid:Equil. Cooling: Ttransf. = 727CDTUndercooling by Ttransf. < 727C0.760.0221718Rate of Phase TransformationAvrami equation => y = 1- exp (-kt n)

transformation complete log tFraction transformed, yFixed Tfraction transformedtime0.5By convention rate = 1 / t0.5Fraction transformed depends on timemaximum rate reached now amount unconverted decreases so rate slowst0.5rate increases as surface area increases & nuclei growAvrami relationship - the rate is defined as the inverse of the time to complete half of the transformation. This describes most solid-state transformations that involve diffusion.18S.A. = surface areaIn general, rate increases as T r = 1/t0.5 = A e -Q/RT

R = gas constantT = temperature (K)A = preexponential rate factorQ = activation energyr is often small so equilibrium is not possible.Arrhenius expressionAdapted from Fig. 10.11, Callister 7e. (Fig. 10.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)

135C119C113C102C88C43C110102104Temperature Dependence of Transformation Rate19Generation of Isothermal Transformation Diagrams The Fe-Fe3C system, for Co = 0.76 wt% C A transformation temperature of 675C.1005001102104T = 675C% transformedtime (s)4005006007001101021031041050%pearlite100%50%Austenite (stable)TE (727C)Austenite (unstable)PearliteT(C)time (s)isothermal transformation at 675CConsider:20Coarse pearlite formed at higher temperatures relatively softFine pearlite formed at lower temperatures relatively hard Transformation of austenite to pearlite:gaaaaaapearlite growth directionAustenite (g)grain boundary cementite (Fe3C)Ferrite (a)g For this transformation, rate increases with ( DT) [Teutectoid T ].

675C (DT smaller)050% pearlite600C (DT larger)650C100Diffusion of C during transformationaaggaCarbon diffusionEutectoid Transformation Rate ~ DT21

c11f13Isothermal Transformation Diagrams2 solid curves are plotted: one represents the time required at each temperature for the start of the transformation;the other is for transformation completion.The dashed curve corresponds to 50% completion.The austenite to pearlite transformation will occur only if the alloy is supercooled to below the eutectoid temperature (727C).Time for process to complete depends on the temperature.22

c11f14 Eutectoid iron-carbon alloy; composition, Co = 0.76 wt% C Begin at T > 727C Rapidly cool to 625C and hold isothermally.Isothermal Transformation DiagramAustenite-to-Pearlite23Transformations Involving Noneutectoid CompositionsHypereutectoid composition proeutectoid cementiteConsider C0 = 1.13 wt% CFe3C (cementite)160014001200100080060040001234566.7Lg (austenite)g+Lg +Fe3Ca +Fe3CL+Fe3Cd(Fe)C, wt%CT(C)727CDT0.760.0221.132425Transformations Involving Noneutectoid CompositionsHypereutectoid composition proeutectoid cementiteConsider C0 = 1.13 wt% CaTE (727C)T(C)time (s)AAA+CP110102103104500700900600800A+PAdapted from Fig. 11.16, Callister & Rethwisch 3e. Adapted from Fig. 10.28, Callister & Rethwisch 3e. Fe3C (cementite)160014001200100080060040001234566.7Lg (austenite)g+Lg +Fe3Ca +Fe3CL+Fe3Cd(Fe)C, wt%CT(C)727CDT0.760.0221.1325


c11f37StrengthDuctilityMartensite T Martensite bainite fine pearlite coarse pearlite spheroiditeGeneral TrendsPossible Transformations 27

Coarse pearlite (high diffusion rate) and (b) fine pearlitec11f15

2810103105time (s)10-1400600800T(C)Austenite (stable)200PBTE0%100%50%AABainite: Non-Equil Transformation Products elongated Fe3C particles in a-ferrite matrix diffusion controlled a lathes (strips) with long rods of Fe3C 100% bainite100% pearlite

MartensiteCementiteFerrite29Bainite Microstructure Bainite consists of acicular (needle-like) ferrite with very small cementite particles dispersed throughout. The carbon content is typically greater than 0.1%. Bainite transforms to iron and cementite with sufficient time and temperature (considered semi-stable below 150C).

3010 Fe3C particles within an a-ferrite matrix diffusion dependent heat bainite or pearlite at temperature just below eutectoid for long times driving force reduction of a-ferrite/Fe3C interfacial areaSpheroidite: Nonequilibrium Transformation


c11f20Pearlitic Steel partially transformed to Spheroidite32 single phase body centered tetragonal (BCT) crystal structure BCT if C0 > 0.15 wt% C Diffusionless transformation BCT few slip planes hard, brittle% transformation depends only on T of rapid cooling

Martensite Formation Isothermal Transformation Diagram10103105time (s)10-1400600800T(C)Austenite (stable)200PBTE0%100%50%AAM + AM + AM + A0%50%90%Martensite needlesAustenite

33An micrograph of austenite th