Phase Transformation

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Phase Transformation Chapter 9 Shiva-Parvati, Chola BronzeBall State UniversityQ: How was the statue made?A: Invest castingLiquid-to-solid transformationAn example of phase transformation Czochralski crystal pulling technique for single crystal Si Quenching of steel componentsa solid->solid phase transformation LiquidsolidificationevaporationsublimationSolidgasmeltingcondensationSolid state phase transformationSolid 2 1 Thermodynamic driving force for a phase transformationDecrease in Gibbs free energyLiquid-> solidgs - gl = g = -ve ggLgSgS < gLgL < gSLiquid is stableTmTGibbs free energy as a function of temperature, Problem 2.3gLgS gSolid is stableTfreesingsTgp


.|TcTg pp


.|22Fig. 9.1 How does solidification begins?Usually at the walls of the containerWhy?To be discussed later.Heterogeneous nucleation. Spherical ball of solid of radius R in the middle of the liquid at a temperature below TmHomogeneous nucleationgL = free energy of liquid per unit volumegS = free energy of solid per unit volumer g = gS- gL Change in free energy of the system due to formation of the solid ball of radius r :r) (343L s g g r f +ve: barrier to nucleation 24 r +) (343L s g g r rr*f 24 r+ g r f 334 24 r +g r 334rr*f 24 r+Solid balls of radius r < r* cannot grow as it will lead to increase in the free energy of the system !!!Solid balls of radii r > r* will growr* is known as the CRITICAL RADIUS OF HOMOGENEOUS NUCLEATION g r f 334 24 r +g r 334rr*f 24 r+0* r rrfgr 2** f 23) ( 316*gf Eqn. 9.5Eqn. 9.4 TgTmgL gST g (T)L S g g g ) ( ) ( ) ( T s T T h T g ) ( ) ( mT h T h ) ( ) ( mT s T s 0 ) ( ) ( ) ( m m m m T s T T h T gmmmTT hT s) () ( ) ( ) ( ) ( m m T s T T h T g mmmTT hT T h) () ( ) ( mmmT hT T Tmm hTTT g ) (Eqn. 9.7 g r f 334 24 r+gr 2*23) ( 316*gf ) (34) (3T g r T f 24 r+ frmm hTTT g ) (mmh T Tr 2*2 22 3) ( ) ( 316*mmh T Tf Eqn. 9.8Eqn. 9.7Fig. 9.3r1* f1* f2*r2*T1T2 < Critical particleFig. 9.4Formation of critical nucleus by statistical flucctuationAtoms surrounding the critical particleDiffuse jump of a surrounding atom to the critical particle makes it a nucleation The Nucleation RateNt=total number of clusters of atoms per unit volumeN* = number of clusters of critical size per unit volumeBy Maxwell-Boltzmann statistics


.| RTfN N t*exp *


.| RTfN N t*exp *s*= no. of liquid phase atoms facing the critical sized particle Hd = activation energy for diffusive jump from liquid to the solid phase = atomic vibration frequencyThe rate of successful addition of an atom to a critical sized paticle


.| RTHs v dexp * ' Eqn. 9.10Eqn. 9.9 Rate of nucleation, I , (m3s-1(' * N I ]]]

+ RT H fs N dt*exp *With decreasing T 1. Driving force increases2. Atomic mobility decreases= No. of nucleation events per m3 per sec= number of critical clusters per unit volume (N*)x rate of successful addition of an atom to the critical cluster ( )




.| RTHsRTfN dtexp **exp Eqn. 9.11 TITm GrowthIncrease in the size of a product particle after it has nucleateddtdrU TU Overall Transformation Kinetics) , ( I U fdTdXUIdX/dtTI : Nucleation rateU : Growth ratedtdrOverall transformation rate (fraction transformed per second) X=fraction of product phase Fraction transformed as a function of timets tfXtSlow due to very few nucleiSlow due to final impingement TTT Diagram for liquid-to-solid transformationTStable liquidUnderCooled liquidcrystalCrystallization beginsL+Crystallization endsdX/dtTlog tXlog t tstf01TmC-curves L+TStable liquidUnderCooled liquidlog tTmTTT Diagram for liquid-to-solid transformationUITCoarse grained crystalsFine grained crystalsglass Tlog tts metalsts SiO2]]]

+ RT H fs N I dt*exp *2 22 3) ( ) ( 316*mmh T Tf Hd log (viscosity)Metals: high hm, low viscosity SiO2: low hm, high viscosity Silica glassMetallic glassEqn. 9.11 Eqn. 9.8 Cooling rate 106 C s-1Inert gas pressureMolten alloyHeater coilQuartz tubeRotating cooledmetal drumJet of molten metalRibbon ofglassy metalFrom Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002(http://Materials.Usask.CaMelt Spinning for metallic glass ribbons L+Tlog tTmTTmTgLog (viscosity)1218crystalStable liquidUndercooled liquidglass30Fig. 9.17 TmSpecific volumeStable liquidUndercooled liquidFast coolSlow coolTgsTgfcrystalFig. 9.18T log tUITL+TStable liquidUndercooled liquidTmdevitrificationtimeTGlass ceramicsnucleationgrowthglass Glass ceramicLiquidglasscrystalVery fine crystals Cornings new digital hot plates with PyroceramTM tops. Corningware PyroceramTM heat resistant cookwareROBAX was heated until red-hot. Then cold water was poured on the glass ceramic from above - with NO breakage. Czochralski crystal pulling technique for single crystal SiSSPL: Solid State Physics Laboratory, N. DelhiJ. Czochralski, (1885-1953)Polish Metallurgist You may collect slide handouts for chapters 6, 7 and 8 from Scoops Xerox Shopno more grades, no more pencils,no more sharing/using stencils,no more reading, no more books,no more teachers dirty looks,so when we hear that final bell,we drop our books and run like hell !! ASteelHardnessRockwell C15 0.8Wt% CMicro-structureCoarsepearlitefinepearlitebainiteTempered martensitemartensite0. 9.2 HEAT TREATMENTHeating a material to a high temperature, holding it at that temperature for certain length of time followed by cooling at a specified rate is called heat treatment ANATTQheatingholdingtimeTAnnealing Furnace cooling RC 15Normalizing Air cooling RC 30Quenching Water cooling RC 65Tempering Heating after quench RC 55Austempering Quench to an inter- RC 45mediate temp and hold Eutectoid ReactionC FeCo3725+ 0.8 0.02 6.67coolPearliteAmmount of Fe3C in PearliteRed Tie Line below eutectoid temp117 . 065 . 678 . 002 . 0 67 . 602 . 0 8 . 03 pearliteC Ff Phase diagrams do not have any information about time or rates of transformations.We need TTT diagram for austenite-> pearlite transformation Stable austeniteunstable austeniteTTT diagram for eutectoid steelstartfinish Stable austeniteunstable austenitestartfinishAnnealing:coarse pearliteNormalizing:fine pearliteUITTTT diagram for eutectoid steel Callister Stable austeniteunstable austenitestartfinishTTT diagram for eutectoid steelA+MMMsMfMs : Martensite start temperatureMf : Martensite finish temperature : martensite (M)' cooling rapidQUENCHINGHardness RC 65Extremely rapid, no C-curves BCTAmount of martensite formed does not depend upon time, only on temperature.Atoms move only a fraction of atomic distance during the transformation:1. Diffusionless (no long-range diffusion)2. Shear (one-to-one correspondence between and atoms) 3. No composition changeMartensitic transformation Problem 3.1BCT unit cell of (austenite)414 . 1 2 acBCT unit cell of (martensite)08 . 1 00 . 1 ac0% C (BCC) 1.2 % C Contract ~ 20%Expand ~ 12%Martensitic transformation (contd.)Fig. 9.12 Hardness of martensite as a function of C contentWt % Carbon 2040600.2 0.4 0.6Hardness, RCHardness of martensite depends mainly on C content and not on other alloying additionsFig. 9.13Martensitic transformation (contd.) ANATTQheatingT Heating of quenched steel below the eutectoid temperature, holding for a specified time followed by ar cooling. TEMPERINGC Fetempering3+ T higher ductility, lower strength Tempering ContinuedCallister AustemperingBainiteShort needles of Fe3C embedded in plates of ferrite Problems in QuenchingQuench CracksHigh rate of cooling:surface cooler than interiorSurface forms martensite before the interiorAustenite martensite Volume expansionWhen interior transforms, the hard outer martensitic shell constrains this expansion leading to residual stresses But how to shift the C-curve to higher times?Solution to Quench cracksShift the C-curve to the right (higher times)More time at the noseSlower quenching (oil quench) can give martensite By alloyingAll alloying elements in steel (Cr, Mn, Mo, Ni, Ti, W, V) etc shift the C-curves to the right.Exception: CoSubstitutional diffusion of alloying elements is slower than the interstitial diffusion of C Plain C steelAlloy steelAlloying shifts the C-curves to the right.Separate C-curves for pearlite and bainiteFig. 9.10 HardenabilityAbility or ease of hardening a steel by formation of martensite using as slow quenching as possibleAlloying elements in steels shift the C-curve to the rightAlloy steels have higher hardenability than plain C steels. Hardnenability HardnessAbility or ease of hardening a steelResistance to plastic deformation as measured by indentationOnly applicable to steels Applicable to all materialsAlloying additions increase the hardenability of steels but not the hardness.C increases both hardenability and hardness of steels. High Speed steelAlloy steels used for cutting tools operated at high speedsCutting at high speeds lead to excessive heating of cutting toolsThis is equivalent to unintended tempering of the tools leading to loss of hardness and cutting edgeAlloying by W gives fine distribution of hard WC particles which counters this reduction in hardness: such steels are known as high speed steels. Airbus A380 to be launched on October 2007 A shop inside Airbus A380 Alfred Wilms Laboratory 1906-1909Steels harden by quenchingWhy not harden Al alloys also by quenching? timeWilms Plan for hardening Al-4%Cu alloySorry! No increase in hardness.550CTHeatQuenchHoldCheck hardnessEureka ! Hardness has In