Phase Transformations

PHASE TRANSFORMATIONS Nucleation Growth APPLICATIONS Transformations in Steel Precipitation Solidification & crystallization Glass transition Recovery, Recrystallization & Grain growth Phase Transformations in Metals and AlloysDavid Porter & Kenneth Esterling Van Nostrand Reinhold Co. Ltd., New York (1981)

DiffusionalPHASE TRANSFORMATIONSMartensitic1nd order nucleation & growthPHASE TRANSFORMATIONS2nd order Entire volume transformsBased onMasstransportBased onorder

Energies involvedBulk Gibbs free energy Interfacial energy Strain energy Solid-solid transformationVolume of transforming materialNew interface created The concepts are illustrated using solidification of a metal

Nucleation of phaseTrasformation +Growth till is exhausted=1nd order nucleation & growth

Liquid Solid phase transformationSolid (GS)Liquid (GL)TmT G TGLiquid stableSolid stableT - Undercooling tFor sufficientUndercooling On cooling just below Tm solid becomes stable But solidification does not start E.g. liquid Ni can be undercooled 250 K below TmG veG +ve

Nucleation The probability of nucleation occurring at point in the parent phase is same throughout the parent phase In heterogeneous nucleation there are some preferred sites in the parent phase where nucleation can occurHomogenousHeterogenousNucleationNucleationSolidification+Growth= Liquid solid walls of container, inclusions Solid solid inclusions, grain boundaries, dislocations, stacking faults

Homogenous nucleationr2r31Neglected in L Stransformations

By setting dG/dr = 0 the critical values (corresponding to the maximum) are obtained (denoted by superscript *) Reduction in free energy is obtained only after r0 is obtainedTrivialAs Gv is ve, r*is +ver G Supercritical nucleiEmbryos

The bulk free energy reduction is a function of undercooling r G Increasing TDecreasing r*Decreasing G*TmTurnbull approximation

No. of critical sized particlesRate of nucleationxFrequency with which they become supercritical=Critical sized nucleuss* atoms of the liquid facing the nucleusCritical sized nucleusJump taking particle to supercriticality nucleated (enthalpy of activation = Hd)No. of particles/volume in L lattice vibration frequency (~1013 /s)

I T (K) Increasing TTm0T = Tm G* = I = 0 G* I T I T = 0 I = 0

Heterogeneous nucleationConsider the nucleation of from on a planar surface of inclusion Alens Acircle Acircle CreatedCreatedLostSurface tension force balanceInterfacial EnergiesVlens = h2(3r-h)/3Alens = 2rhh = (1-Cos)rrcircle = r Sin

(degrees) G*hetero / G*homo G*hetero (0o) = 0 no barrier to nucleationG*hetero (90o) = G*homo/2 G*hetero (180o) = G*homo no benefitComplete wettingNo wettingPartial wetting

= f(number of nucleation sites)~ 1042= f(number of nucleation sites)~ 1026BUT the exponential term dominatesIhetero > Ihomo

Choice of heterogeneous nucleating agent Small value of Choosing a nucleating agent with a low value of (low energy interface) (Actually the value of ( ) will determine the effectiveness of the heterogeneous nucleating agent high or low ) low value of Crystal structure of and are similar and lattice parameters are as close as possible Seeding rain-bearing clouds AgI or NaCl nucleation of ice crystals Ni (FCC, a = 3.52 ) is used a heterogeneous nucleating agent in the production of artificial diamonds (FCC, a = 3.57 ) from graphite

Nucleation of phaseTrasformation +Growth till is exhausted= At transformation temperature the probability of jump of atom from (across the interface) is same as the reverse jump Growth proceeds below the transformation temperature, wherein the activation barrier for the reverse jump is higherGrowth

I, U, T T (K) Increasing TTm0UT I Maximum of growth rate usually at higher temperature than maximum of nucleation rate

Time Temperature Transformation (TTT) diagramsA type of phase diagramT (rate sec1) T (K) TTm0t (sec) T (K) Tm0Time for transformationSmall driving force for nucleationGrowth sluggishReplot

t (sec) T (K) 99% = finishIncreasing % transformationTTT diagram phase transformation1% = start

T G Turnbulls approximationTmSolid (GS)Liquid (GL)TG

APPLICATIONSPhase Transformations in SteelPrecipitationSolidification and crystallizationGlass transitionRecovery recrystallization & grain growth

Phase Transformations in Steel

%C T FeFe3C6.74.30.80.162.06PeritecticL + Eutectic L + Fe3CEutectoid + Fe3CLL + + Fe3C1493C1147C723CFe-Cementite diagram 0.025 %C0.1 %C + Fe3C

AusteniteAustenitePearlitePearlite + BainiteBainiteMartensite1002003004006005008007230.1110102103104105Eutectoid temperatureNot an isothermal transformationMsMfCoarseFinet (s) T Time- Temperature-Transformation (TTT) Curves Isothermal TransformationEutectoid steel (0.8%C)

AustenitePearlitePearlite + BainiteBainiteMartensite1002003004006005008007230.1110102103104105Eutectoid temperatureMsMft (s) T Time- Temperature-Transformation (TTT) Curves Isothermal TransformationEutectoid steel (0.8%C) + Fe3C

Continuous Cooling Transformation (CCT) CurvesEutectoid steel (0.8%C)AusteniteMartensite1002003004006005008007230.1110102103104105Eutectoid temperatureMsMft (s) T Original TTT linesCooling curves Constant ratePearlite

Eutectoid steel (0.8%C)1002003004006005008007230.1110102103104105t (s) T Water quenchOil quenchNormalizingFull annealDifferent cooling treatments M = MartensiteP = PearliteCoarse P P MM+Fine P

Pearlite Nucleation and growth Heterogeneous nucleation at grain boundaries Interlamellar spacing is a function of the temperature of transformation Lower temperature finer spacing higher hardness + Fe3C[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962 [1][1]

Bainite Nucleation and growth Acicular, accompanied by surface distortions** Lower temperature carbide could be carbide (hexagonal structure, 8.4% C) Bainite plates have irrational habit planes Ferrite in Bainite plates possess different orientation relationship relative to the parent Austenite than does the Ferrite in Pearlite + Fe3C**Bainite formed at 348oCBainite formed at 278oC[1] Physical Metallurgy for Engineers by Donald S Clark and Wilbur R Varney (Second Edition) Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962 [1][1]

MartensiteFCCAusteniteFCCAusteniteAlternate choice of CellTetragonal MartensiteAustenite to Martensite 4.3 % volume increasePossible positions of Carbon atomsOnly a fraction of the sites occupied20% contraction of c-axis12% expansion of a-axisRefer Fig.9.11 in textbookIn Pure Fe after the Matensitic transformationc = aC along the c-axis obstructs the contraction

Martensite The martensitic transformation occurs without composition change The transformation occurs by shear without need for diffusion The atomic movements required are only a fraction of the interatomic spacing The shear changes the shape of the transforming region results in considerable amount of shear energy plate-like shape of Martensite The amount of martensite formed is a function of the temperature to which the sample is quenched and not of time Hardness of martensite is a function of the carbon content but high hardness steel is very brittle as martensite is brittle Steel is reheated to increase its ductility this process is called TEMPERING

% Carbon Hardness (Rc) 2040600.20.40.6Harness of Martensite as a function of Carbon content

Properties of 0.8% C steelConstituentHardness (Rc)Tensile strength (MN / m2)Coarse pearlite16710Fine pearlite30990Bainite451470Martensite65-Martensite tempered at 250 oC551990

Tempering Heat below Eutectoid temperature wait slow coolingThe microstructural changes which take place during tempering are very complex Time temperature cycle chosen to optimize strength and toughness Tool steel: As quenched (Rc 65) Tempered (Rc 45-55)

MARTEMPERINGAUSTEMPERING To avoid residual stresses generated during quenching Austenized steel is quenched above Ms for homogenization of temperature across the sample The steel is then quenched and the entire sample transforms simultaneously Tempering follows To avoid residual stresses generated during quenching Austenized steel is quenched above Ms Held long enough for transformation to BainiteMartemperingAustempering

ALLOY STEELS Various elements like Cr, Mn, Ni, W, Mo etc are added to plain carbon steels to create alloy steels The alloys elements move the nose of the TTT diagram to the right this implies that a slower cooling rate can be employed to obtain martensite increased HARDENABILITY The C curves for pearlite and bainite transformations overlap in the case of plain carbon steels in alloy steels pearlite and bainite transformations can be represented by separate C curves

ROLE OF ALLOYING ELEMENTS + Simplicity of heat treatment and lower cost Low hardenability Loss of hardness on tempering Low corrosion and oxidation resistance Low strength at high temperaturesPlain Carbon SteelElement AddedSegregation / phase separationSolid solutionCompound (new crystal structure) hardenability Provide a fine distribution of alloy carbides during tempering resistance to softening on tempering corrosion and oxidation resistance strength at high temperatures Strengthen steels that cannot be quenched Make easier to obtain the properties throughout a larger section Elastic limit (no increase in toughness)Alloying elements Alter temperature at which the transformation occurs Alter solubility of C in or Iron Alter the rate of various reactionsInterstitialSubstitutional

AustenitePearliteBainiteMartensite100200300400600500800MsMft T TTT diagram for Ni-Cr-Mo low alloy steel~1 min

Precipitation

The presence of dislocation weakens the crystal easy plastic deformation Putting hindrance to dislocation motion increases the strength of the crystal Fine precipitates dispersed in the matrix provide such an impediment Strength of Al 100 MPa Strength of Duralumin (Al + 4% Cu + other alloying elements) 500 MPa

4 % Cu + + Slow equilibrium cooling gives rise to coarse precipitates which is not good in impeding dislocation motion.**Also refer section on Double Ended Frank-Read Source in the chapter on plasticity: max = Gb/L

CABHeat (to 550oC) solid solution Quench (to RT) Age (reheat to 200oC) fine precipitatesCABTo obtain a fine distribution of precipitates the cycle A B C is usedNote: Treatments A, B, C are for the same compositionsupersaturated solutionIncreased vacancy concentration

Log(t) Hardness 180oC100oC20oC Higher temperature less time of aging to obtain peak hardness Lower temperature increased peak hardness optimization between time and hardness required

Log(t) Hardness 180oCTmOveragedUnderagedPeak-agedRegion of solid solution strengthening (no precipitation hardening)Region of precipitation hardening (but little solid solution strengthening)Dispersion of fine precipitates (closely spaced)Coarsening of precipitates with increased interparticle spacing

Log(t) Hardness 180oCPeak-agedParticle radius (r) CRSS Increase Particle shearingParticle By-passCoherent (GP zones)In-coherent (precipitates)

Due to large surface to volume ratio the fine precipitates have a tendency to coarsen small particles dissolve and large particles grow Coarsening in number of particles in interparticle spacing reduced hindrance to dislocation motion (max = Gb/L)

Solidification and Crystallization

Hfusion Hd Log [Viscosity ()]Crystallization favoured byHigh (10-15) kJ / moleLow (1-10) PoiseMetalsEnthalpy of activation for diffusion across the interfaceDifficult to amorphize metalsThermodynamicKineticVery fast cooling rates ~106 K/s are used for the amorphization of alloys splat cooling, melt-spinning.

Fine grain size bestows superior mechanical properties on the material High nucleation rate and slow growth rate fine grain size Cooling rate lesser time at temperatures near Tm , where the peak of growth rate (U) lies nucleation rate Cooling rates ~ (105 106) K/s are usually employed Grain refinement can also be achieved by using external nucleating agents Single crystals can be grown by pulling a seed crystal out of the meltI, U T (K) Tm0U I

Hfusion Hd Log [Viscosity ()]Crystallization favoured bylowHigh (1000) PoiseSilicatesEnthalpy of activation for diffusion across the interfaceEasily amorphizedThermodynamicKineticCertain oxides can be added to silica to promote crystallization

In contrast to metals silicates, borates and phosphates tend to form glasses Due to high cation-cation repulsion these materials have open structures In silicates the difference in total bond energy between periodic and aperiodic array is small (bond energy is primarily determined by the first neighbours of the central cation within the unit

A composite material of glass and ceramic (crystals) can have better thermal and mechanical properties But glass itself is easier to form (shape into desired geometry)Glass-ceramic (pyroceram)Shaping of material in glassy stateHeterogenous nucleating agents (e.g. TiO2) added (dissolved) to molten glassTiO2 is precipitated as fine particlesHeld at temperature of maximum nucleation rate (I)Heated to temperature of maximum growth rate

Even at the end of the heat treatment the material is not fully crystalline Fine crystals are embedded in a glassy matrix Crystal size ~ 0.1 m (typical grain size in a metal ~ 10 m) Ultrafine grain size good mechanical properties and thermal shock resistance Cookware made of pyroceram can be heated directly on flame

Glass Transition

All materials would amorphize on cooling unless crystallization intervenesT Volume Or other extensive thermodynamic property S, H, ELiquidGlassCrystalTgTmGlass transition temperature

T Volume Change in slopeTfFictive temperature (temperature at which glass is metastable if quenched instantaneously to this temperature) can be taken as Tg

T Volume Effect of rate of coolingSlower coolingSlower coolingHigher densityLower TgLower volumeAs more time for atoms to arrange in closer packed configuration

T Log (viscosity) GlassCrystalTgTmSupercooled liquidLiquid On crystallization the viscosity abruptly changes from ~100 ~1020 Pa s A solid can be defined a material with a viscosity > 1012 Poise

TgHeat glassCool liquidTxOften metallic glasses crystallize before Tg

Please read up paragraph on glassy polymers p228 in text book

Recovery, Recrystallization & Grain Growth

Cold work dislocation density point defect densityPlastic deformation in the temperature range (0.3 0.5) Tm COLD WORK Point defects and dislocations have strain energy associated with them (1 -10) % of the energy expended in plastic deformation is stored in the form of strain energy

Cold work dislocation density point defect densityAnnealMaterial tends to lose the stored strain energyIncrease in strength of the materialSoftening of the materialCold workAnnealRecrystallizationRecoveryLow temperatureHigh temperature

Cold workAnnealRecrystallizationRecoveryGrain growth

Cold work Hardness Strength Changes occur to almost all physical and mechanical properties X-Ray diffration Laue patterns of single crystals show pronounced asterism due to lattice curvatures Debye-Scherrer photographs show line broadning Residual stresses + deformations

Electrical resistance Ductility

Recovery Recovery takes place at low temperatures of annealing Apparently no change in microstructure Excess point defects created during Cold work are absorbed: at surface or grain boundaries by dislocation climb Random dislocations of opposite sign come together and annihilate each other Dislocations of same sign arrange into low energy configurations: Edge Tilt boundaries Screw Twist boundaries POLYGONIZATION Overall reduction in dislocation density is small

POLYGONIZATIONBent crystalLow angle grain boundariesPolygonization

Recrystallization Trecrystallization (0.3 0.5) Tm Nucleation and growth of new, strain free crystals Nucleation of new grains in the usual sense may not be present and grain boundary migrates into a region of higher dislocation density G (recrystallization) = G (deformed material) G (undeformed material) TRecrystallization is the temperature at which 50 % of the material recrystallizes in 1 hourRegion of lower dislocation densityRegion of higher dislocation densityDirection of grain boundary migration

Further points about recrystallization Deformation recrystallization temperature (Trecrystallization) Initial grain size recrystallization temperature High cold work + low initial grain size finer recrystallized grains cold work temperature lower strain energy stored recrystallization temperature Rate of recrystallization = exponential function of temperature Trecrystallization = strong function of the purity of the material Trecrystallization (very pure materials) ~ 0.3 Tm Trecrystallization (impure) ~ (0.5 0.6) Tm Trecrystallization (99.999% pure Al) ~ 75oC Trecrystallization (commercial purity) ~ 275oC The impurity atoms segregate to the grain boundary and retard their motion Solute drag (can be used to retain strength of materials at high temperatures)

The impurity atoms seggregate to the grain boundary and retard their motion Solute drag (can be used to retain strength of materials at high temperatures) Second phase particles also pin down the grain boundary during its migration

Hot Work and Cold Work Hot Work Plastic deformation above TRecrystallization Cold Work Plastic deformation below TRecrystallizationCold WorkHot WorkRecrystallization temperature (~ 0.4 Tm)

Grain growth Globally Driven by reduction in grain boundary energy Locally Driven by bond maximization (coordination number maximization)

Direction of grain boundary migrationBoundary moves towards its centre of curvatureJUMP

Cold workRecoveryRecrystallizationGrain growthTensile strengthDuctilityElectical conductivityInternal stress

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Phase Transformations