LECTURE NOTES ON - VSSUT
LECTURE NOTES ONMMMM-1515--036 : PHASE TRANSFORMATIONS5th Semester, MME
MMMM--1515--036PHASE TRANSFORMATIONSCourse CoordinatorAvala Lava KumarDepartment of Metallurgical & Materials Engineering (MME)Veer Surendra Sai University of Technology (VSSUT), Burla-768018E-mail : lavakumar.vssut@gmail.com Phone: ( 91) (7077110110)Suneeti PurohitDepartment of MME, VSSUT, Burla – 768018E-mail : suneeti.purohit@gmail.comPhone : ( 91) 8339037187Dr. S.K.BadjenaDepartment of MME, VSSUT, Burla – 768018E-mail : skbadjena@gmail.comPhone : ( 91) 8455938473
PHASE TRANSFORMATIONSCourse ObjectiveThe aim of this course is to gain an understanding of the role of phase transformations on thedevelopment of microstructure and properties of metallic materials. The course will highlight anumber of commercially-significant applications where phase transformations are important.Course OverviewNucleation in the liquid and solid states; thermodynamics of phase transformations;solidification of pure metals and alloys; thermal supercooling; constitutional supercooling;interface stability; solute redistribution; Solid state transformations : nucleation and growth ofphases; diffusion mechanisms; transformation kinetics; transformation diagrams. Diffusionaland Diffusionless transformations: decomposition of solid solutions; ordering reactions,spinodal decomposition; eutectoid, bainitic and martensitic transformations. Aspects of ferrousmetallurgy and common classes of low carbon and alloy steels to be taught illustratingsome of the principles involved.Learning OutcomesEnhanced critical thinking, analytical and problem solving skills in materials science andengineering. An understanding of the principles underlying liquid-to solid and solid-state phasetransformations in a range of materials. An understanding of the importance of phasetransformations for controlling microstructure and properties in engineering alloys.
MMMM--1515--036 : PHASE TRANSFORMATIONSCONTENTSChapterChapter NamePage No1Introduction2Thermodynamics & Kinetics3Diffusion96 – 1804Interfaces in Materials181 – 2125Solidification213 – 2466Diffusional Transformations247 – 324Diffusionless Transformations325 – 341Recovery Recrystallization and Graingrowth342 - 35676 -1516 - 95
INTRODUCTION TO PHYSICAL METALLURGYREFERENCES Phase Transformations in Metals and Alloys (This is the major reference for this course)D.A.Porter, K.E. Easterling, and M.Y. SharifCRC Press , Taylor & Francis Group Diffusion in solidsProf. Alok Paul , IISC BangloreNPTEL Web course Phase TransformationsProf. Anandh Subramaniam IIT Kanpur Phase Transformations & Heat TreatmentProf. M.P.GururajanNPTEL web course Phase Transformations in MaterialsRomesh C. SharmaCBS Publishers & Distributors Introduction to Physical MetallurgySidney H. AvnerMcGraw Hill Education (India) Pvt Ltd
Avala Lava Kumar : Suneeti Purohit : Dr.S.K.BadjenaDepartment of Metallurgical & Materials Engineering (MME)Veer Surendra Sai University of Technology (VSSUT), Burla -768018*E-mail : lavakumar.vssut@gmail.com6
Entropic CLIDEANSPHERICALENERGYSPACEGRAVITYnD tFIELDSPARTICLESMETALSEMI-METALBAND ATE / NANO-QUASICRYSTALSNANOCRYSTALS7
Classification of materialsMaterialsMonolithicMetals (& Alloys)HybridsComposites: have two (or more)solid components; usually one is amatrix and other is a reinforcementCompositeCeramics & GlassesSandwichPolymers (& Elastomers)LatticeSandwich structures: have amaterial on the surface (oneor more sides) of a corematerialLattice* Structures: typically acombination of material and space(e.g. metallic or ceramic forms,aerogels etc.).SegmentSegmented Structures: aredivided in 1D, 2D or 3D(may consist of one ormore materials).Hybrids aredesigned to improvecertain properties ofmonolithic materials8*Note: this use of the word 'lattice' should not be confused with the use of the word in connection with crystallography.
Length scales in o-mechanicalTreatments Casting Metal Forming Welding Powder Processing MachiningMicrostructureComponentPhases Defects Residual Stress& their distribution Structure could imply two types of structure: Crystal structure Electromagnetic structure Fundamentally these aspects are two sides of the samecoinMicrostructure can be defined as:(Phases Defect Structure Residual Stress) and theirdistributionsMicrostructure can be ‘tailored’ by thermo-mechanicaltreatments Vacancies Dislocations Twins Stacking Faults Grain Boundaries Voids Cracks9Processing determines shape and microstructure of a component
Length scales in metallurgyLet us start with a cursory look at the length scales involved in Materials ScienceAngstromsDislocation Stress fields NanometersMicronsCentimetersUnit Cell*Crystalline DefectsMicrostructureComponentGrain Size*Simple Unit Cells10
Transformations in MaterialsPhasesDefectsResidual stressPhases can transformDefect structures can changePhasetransformationDefect alPropertyPhasesPhases TransformationsStress state can be rostructural Transformations11
Classification of TransformationsThermodynamics Order of a phase transformationClassification ofPhaseTransformationsBased onEhrenfest, 1930ReconstructiveMechanismBuerger, 1951DisplaciveNon-quenchable Athermal RapidKineticsle Chatelier, (Roy 1973)Quenchable Thermal Sluggish12
Classification of Transformations Thethermodynamiccharacteristicsassociated with the phase transformationscan be used to classify transformations; inthis classification methodology, if the nthderivative of free energy (G) with respect totemperature (T) and pressure (P) isdiscontinuous, it is defined as the nth ordertransformation. As shown in Fig., in transformations such asmelting, the first derivative has thediscontinuity; hence, melting is a first ordertransformation; on the other hand, in someof the order/disorder transfor- mations, it isthesecondderivativewhichisdiscontinuous, making it the second ordertransformation.Figure: The thermodynamic classification of transformations:the first derivative of the free energy ‘G’ with respect totemperature ‘T’ , that is the enthalpy ‘H’ is discontinuous at thetransformation temperature Tc as shown in the first column; thesecond derivative of the free energy with respective totemperature Cp is discontinuous while ‘H’ is not in the secondcolumn, making the order of transformation second.13
Classification of TransformationsClassification of TransformationsHeterogeneous Transformations(nucleation and growth)GROWTH CONTROLLEDBY HEAT TRANSFERGROWTH CONTROLLED BYHEAT AND MASS TRANSFERHomogeneous TransformationsSpinodal decompositionOrder-disorder transformationGROWTH CONTROLLED BYTHERMALLY ACTIVATEDMOVEMENTS OF ATOMSSolidification of pure metals Solidification of alloysSHORT RANGE TRANSPORTA THERMALGROWTHMartensitetransformationsLONG RANGE TRANSPORT(interface controlled)Polymeric transformationsMassive transformationsRecrystallizationGrain growth, etc.Continuous ReactionDiscontinuous ReactionPrecipitation dissolutionEutectoid reactions14Discontinuous precipitation
Classification of Transformations Phase transformations can be classified as homogeneous (transformations which take placethrough spinodal mechanism in which transformation takes place throughout the material)and heterogeneous (transformations which take place through nucleation and growthmechanism in which transformation takes place heterogeneously at a few places in thematerial at the start of the transformation). Transformations can also be classified as diffusional (or, so called, civilian') anddiffusionless (or, so called military') depending on the mechanism. In civiliantransformations, the nucleation and growth take place via diffusion assisted atomic motion.On the other hand, in the military transformation, the nucleation and growth is by shear andshuffle of atoms by less than one atomic displacement and the movement of all theparticipating atoms is coordinated. There are transformations which are thermally activated (which typically are based ondiffusion) while there are others which are athermal. The transformations can also be diffusion controlled or interface controlled. Transformations can also be differentiated based on whether the interfaces formed areglissile or nonglissile. In some transformations there are compositional changes while in some other there are nocomposition changes. Further, transformations which are diffusional can either involve long range diffusion or15short range diffusion.
Avala Lava Kumar* : Suneeti Purohit : Dr. S.K.BadjenaDepartment of Metallurgical & Materials Engineering (MME)Veer Surendra Sai University of Technology (VSSUT), Burla -768018*E-mail : lavakumar.vssut@gmail.com16
Introduction The fields of Thermodynamics and Kinetics are vast oceans and this chapter will introducethe bare essentials required to understand the remaining chapters. Let us start by performing the following (thought) experiment:Heat a rod of Al from room temperature to 500 C As expected the rod will expand(A B in figure below). The expansion occurs because of two reasons:1 Vibration of atoms (leading to an increase in average spacing between atoms theusual reason) (A M in figure below). 2 Increase in the concentration of vacancies* (a vacancy is created when a Al atom goesto the surface and for every 4 vacancies created the volume equal to 1 unit cell is added).(M B in figure below). The 2nd reason is a smaller effect in terms of its contribution to theoverall increase in length of the specimenMetal expands onheating due to 2 differentphysical reasons!* It costs energy for the system to put vacancies (broken bonds, distortion to the lattice) then why does the system tolerate vacancies?17
Introduction Now let us perform another (thought) experiment to put in perspective the previousexperiment:Heat a elastomer (cut rubber band) which has been stretched by a small weight by about20 C (room temperature 20 C) the stretched rubber band will contract! The 2nd reason for the expansion of the Al rod is closely related to the contraction of thestretched rubber band! occurs because of thermodynamic reasons (quantities like GibbsFree Energy (G) and Entropy (S)), which we shall learn in this chapter. In the case of the heating of the Al rod- “how the vacancies form” is an issue of kinetics.Kinetics will be dealt with in the topic of kinetics and chapter on Diffusion.A ‘stretched’ elastomercontracts on heating!18
Introduction Let us next consider the melting of a pure metal at its melting point (MP) (atconstant T and P) by supplying heat to the sample of metal (so that the metalsample is only partly molten). At the MP the liquid metal is in equilibrium withthe solid metal. The liquid has higher potential energy as well as higher kinetic energy than thesolid. Then why does the liquid co-exist with the solid? The answer to this question lies in the fact that internal energy is not the measureof stability of the system (under the circumstances). We will learn in this chapter that it is the Gibbs Free Energy (G). The moltenmetal has higher energy (internal energy and enthalpy), but also higher Entropy.So the melting is driven by an increase in Entropy of the system. The moltenmetal and the crystalline solid metal have the same G hence they co-exist inequilibrium.19
Stability and Equilibrium Equilibrium refers to a state wherein there is a balance of ‘forces’* (as we shall seeequilibrium points have zero slope in a energy-parameter plot) Stability relates to perturbations (usually small perturbations** about an equilibrium state)(as we shall see stable relates to the curvature at the equilibrium points). Let us start with a simple mechanical system a rectangular block (Figure in next slide)(under an uniform gravitational potential). The potential energy (PE) of the system depends on the height of the centre of gravity(CG). The system has higher PE when it rests on face-A, than when it rests on face-B. The PE of the system increases when one tilts it from C1 C2 configuration. In configurations such as C1,C2 & C3 the system will be in equilibrium (i.e. will notchange its configuration if there are no perturbations). In configuration C2 the system has the highest energy (point B) and any smallperturbations to the system will take it downhill in energy Unstable state. Configuration C3 has the lowest energy (point C) and the system will return to this state ifthere are small perturbations the Stable state.* Force has been used here in a generalized sense (as an agent which can cause changes)** Perturbation is usually a small ‘force/displacement’ imposed in a short span of time.20
Mechanical Equilibrium of a Rectangular BlockABall on a planeNeutral EquilibriumBCentreOfGravityC2Potential Energy f(height of CG)C1C3BUnstableStableAMetastable stateConfigurationLowest CG of all possiblestatesC21
Stability and Equilibrium Configuration C1 also lies in an ‘energy well’ (like point C) and small perturbations willtend to bring back the system to state C1. However this state is not the ‘global energyminimum and hence is called a Metastable state. Additionally, one can visualize a state of neutral equilibrium, like a ball on a plane(wherein the system is in a constant energy state with respect to configurations). Points to be noted: A system can exist in many states (as seen even for a simple mechanical system: block on a plane) These states could be stable, metastable or unstable Using the relevant (thermodynamic) potential the stability of the system can becharacterized (In the case of the block it is the potential energy, measured by the height of the CG for thecase of the block on the plane) System will ‘evolve’ towards the stable state provided ‘sufficient activation’ is provided(in the current example the system will go from C1 to C3 by ‘sufficient jolting/shaking’ of the plane)Three kinds of equilibrium (with respect to energy) Global minimum STABLE STATE Local minimum METASTABLE STATE Maximum UNSTABLE STATE Constant energy Neutral State/Equilibrium22
Law’s of Thermodynamics Zeroth law of ThermodynamicsIf two systems are each in thermal equilibrium with a third, then all three are inthermal equilibrium with each other. (Similar to the transitive property ofequality in mathematics; i.e. If a b and b c, then a c)IfAB&BCThenACNo heat flowsNo heat flowsNo heat flows(A is in equilibrium with B) (B is in equilibrium with C) (A is in equilibrium with C) First law of ThermodynamicsThis is a statement of the conservation of energy i.e. When heat (Q) is added to asystem, it increases the internal energy (ΔU) of the system and the system doessome work (W) on the external world.Signs of Q and WΔU Q – WFor infinitesimal change of the state,dU δQ – δWQ PositiveSystem gains heatQ PositiveSystem loses heatW PositiveWork done by systemW PositiveWork done on system23
Law’s of Thermodynamics Second law of Thermodynamics:In an isolated system, natural processes are spontaneous when they lead to anincrease in disorder, or entropy i.e. The entropy of a system in an adiabaticenclosure always increases for spontaneous/irreversible processes and remainsconstant during a reversible process but it never decreases.Entropy S is defined by the equationdS δQrevTand is a function of state. Third law of Thermodynamics:The entropy of a perfect crystal is zero when the temperature of the crystal isequal to absolute zero (0 K).lim S 0T 024
Thermodynamic parameters In Materials Science we are mainly interested with condensed matter systems (solids andliquids) (also sometimes with gases) The state of such a system is determined by ‘Potentials’ analogous to the potential energyof the block (which is determined by the centre of gravity (CG) of the block).These potentials are the Thermodynamic Potentials (A thermodynamic potential is aScalar Potential to represent the thermodynamic state of the system). The relevant potential depends on the ‘parameters’ which are being held constant and theparameters which are allowed to change. More technically these are theState/Thermodynamic Variables (A state variable is a precisely measurable physicalproperty which characterizes the state of the system- It does not matter as to how thesystem reached that state). Pressure (P), Volume (V), Temperature (T), Entropy (S) areexamples of state variables. There are 4 important potentials (in some sense of equal stature). These are: InternalEnergy, Enthalpy, Gibbs Free Energy, Helmholtz Free Energy. Intensive properties are those which are independent of the size of the system P, T Extensive Properties are dependent on the quantity of material V, E, H, S, G25
Heat capacity Heat capacity is the amount of heat (measured in Joules or Calories) needed to raise an unitamount of substance (measured in grams or moles) by an unit in temperature (measured in Cor K). This ‘heating’ (addition of energy) can be carried out at constant volume or constant pressure.At constant pressure, some of the heat supplied goes into doing work of expansion and less isavailable with the system (to raise it temperature). Heat capacity at constant Volume (CV): It is the slope of the plot of internal energy with temperature. Heat capacity at constant Pressure (CP): It is the slope of the plot of enthalpy with temperature. Units: Joules/Kelvin/mole, J/K/mole, J/ C/mole, J/ C/g. E CV T V H CP T P Heat capacity is an extensive property (depends on ‘amount of matter’) If a substance has higher heat capacity, then more heat has to be added to raise its temperature.Water with a high heat capacity (of *****) heats up slowly as compared to air (with a heatcapacity, CP 29.07J/K/mole) this implies that oceans will heat up slowly as compared tothe atomosphere. As T 0K, the heat capacity tends to zero. I.e near 0 Kelvin very little heat is required to raisethe temperature of a sample. (This automatically implies that very little heat has to added toraise the temperature of a material close to 0K.26
Internal energy Internal Energy (U or E) Kinetic Energy (KE) Potential Energy (PE)The origin of Kinetic Energy Translations, Rotations, VibrationsThe origin of Potential Energy Bonding between atoms (interactions in the solid)The increase in internal energy on heating from 0 to T Kelvin is given by theequation below; where CV is the specific heat at constant volume and E0 is theinternal energy of the system at 0K. For a cyclic process, change in internal energy (ઢU or ઢE) becomes zero.At constant temperatureAt constant volumeAt constant pressure U U U dV dP f (V , P)T V P P V U U U dP dT f (P,T )V P T T PTU U 0 CV dT0 U U U dV dT f (V ,T ) P V T T V27
Enthalpy Enthalpy (H) Internal Energy PV (work done by the system)Measure of the heat content of the systemAt constant pressure the heat absorbed or evolved is given by HTransformation / reaction will lead to change of enthalpy of systemGaseous state is considered as the reference state with no interactionsFor condensed phases PV E H EThe increase in enthalpy on heating from 0 to T Kelvin is given by the equation below;where CP is the specific heat at constant pressure and H0 is the internal energy of thesystem at 0K (H0 represents energy released when atoms are brought together from the gaseous state to form a solid at zeroKelvin) Enthalpy is usually measured by setting H 0 for a pure element in
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 .
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