Metals And Alloys - Phase Transformations And Complex .
AH1Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaMetals and AlloysThe development of improved metallic materials is a vital activity at the leading edge ofscience and technology. Metals offer unrivalled combinations of properties and reliability at acost which is affordable. They are versatile because subtle changes in their microstructure cancause dramatic variations in their properties. For example, it is possible to buy commercialsteel with a strength as low as 50 MPa or as high as 5500 MPa. An apple weighs about aNewton. The strongest commercial steel can therefore support the weight of about 5.5 109apples on 1 m2 of steel. An understanding of the development of microstructure in metals isessential for the materials scientist. Thus, 70% of all 800 million tonnes per annum of alloysused today were developed in the last ten years.Course A builds on the coverage of metals and alloys in Part IA. Whereas Part IA dealt withthe thermodynamics aspects, we shall emphasize kinetics when treating diffusion, solidificationand solid–state phenomena:Diffusion1. Fundamentals of Diffusion. Diffusive flux and the diffusion equation. Diffusion distances.Mechanisms of diffusion. Interstitial, substitutional and vacancy diffusion. Activation energiesand vacancy concentrations. Diffusivity data. Interdiffusion in alloys. Kirkendall effect.2. Diffusion and Microstructure. Fast diffusion paths. Grain–boundary, free–surface and latticediffusion. Thermodynamics of diffusion. Chemical potential and atomic mobility. Ideal andnon–ideal solutions. Concept of zero, negative diffusivity and uphill diffusion.Solidification3. Undercooling and driving force. Nucleation and crystal growth. Heat flow. Solute partitioning.Effect of convection. The Scheil equation.4. Solidification Structure. Constitutional undercooling, cells and dendrites. Microsegregationprofiles. Coring and non-equilibrium second phase. Grain structures, single crystals andpolycrystals.5. Solidification Processing. Casting. Porosity and hot tearing. Sand casting. Permanent mouldcasting. Centrifugal casting. Continuous casting. Rapid solidification processing, atomisation,melt–spinning.Solid–State Diffusional Transformations6. Dislocations and Grain Boundaries. Cold–worked structures. Stored strain energies. Forcesbetween dislocations. Recovery processes, glide and climb. Polygonisation. Grain boundariesmisorientation, structure and energy.7. Evolution of Grain Structure. Nucleation of recrystallised grains, role of dislocation density.Particle-stimulated nucleation. Mobility of high-angle grain boundaries. Solute drag and Zenerdrag. Grain growth.8. Precipitation. Solution treatment, quenching and ageing. Precipitate nucleation. Precipitationsequences. Diffusion–controlled growth. Nucleation sites. Role of vacancies. Precipitate–freezones, solute and vacancy depletion.
AH2Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaDiffusionless Solid–State Transformations9. Shear Transformations. Twinning, the twin plane and twinning shear. Twinning as a deformation mode. Factors favouring deformation twinning. Strain–rate and crystal–symmetryeffects. Boundary energies. Martensitic transformations. Examples in cobalt and Fe–C. Theshape–memory effect.Some Metallic Materials10. Ferrous Alloys. The Fe–C phase diagram. The eutectoid reaction. Fe–C martensite. TTTcurves. Quenching and tempering of steels. Alloying effects and hardenability. The Jominyend–quench test. Widmanstätten ferrite and bainite. Secondary hardening in alloy steels.11. TRIP steels. Dual–phase steels. Cast irons, grey, white and spheroidal graphitic. Light Alloys.Aluminium alloys. High-strength alloys.12. High–Temperature Alloys. Nickel–based superalloys. Columnar and single–crystal turbineblades. Dispersion–strengthened alloys. Mechanically alloyed systems.Aids to Learning1. D. A. Porter and K. E Easterling, Phase Transformations in Metals and Alloys, 2nd editionChapman and Hall, (1992)[Ln30]2. A. H. Cottrell, An Introduction to Metallurgy, The Institute of Materials, (1995)[A116]3. R. W. K. Honeycombe and H. K. D. H. Bhadeshia, Steels, Microstructure and Properties, 2ndedition, Arnold, (1995)[De88]4. I. J. Polmear, Light Alloys - Metallurgy of the Light Metals, 3rd edition, Arnold, (1995) [Eb153]5. There are a number of metallographic samples associated with this course. They will be referenced in the question sheets. You will find it useful to examine these in the Class Laboratory.Be sure to handle these specimens carefully and to examine them at a variety of magnifications.Try and understand the microstructure in terms of the phase diagrams. A list of the samplesis included below; you will find relevant phase diagrams in your Data Book.CodeComposition / wt%ConditionEtchantM0Fe-0.8C1200 C 2 h, furnace coolednitalM7Al-12Sias–cast in metal mouldnot etchedM8Al–12Si–0.02Naas–cast in metal mouldnot etchedM24Al–4Cusolution treated and over–agedNaOH
AH3Materials Science and Metallurgy, 2nd year courseH. K. D. H. Bhadeshia6. There is a Departmental Electronic Library which can be accessed on the world wide web.This contains useful additional material for this course. The material relevant to Course A islisted below, and there are regular additions to the contents:On–line Teaching Library (Course lLecture notes, question sheets & handoutsWorked ExamplesInternet SupervisorMicrostructure of aluminium-copper alloysMicrostructure of aluminium-silicon alloysDecarburization microstructuresRecrystallisation microstructuresAnnealing twinsPrecipitate-free zonesDendritic solidificationRecrystallised grain sizeMovies showing grain coarseningComputer-generated movies of transformationsActual movies of solidification
AH4Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaFundamentals of DiffusionThe steady–state diffusive flux J is represented using Fick’s first law, CJ D xwhere C is the concentration, x is a distance and D is the diffusion coefficient. Fick’s secondlaw is for cases where the concentration at any point varies with time t: C 2C D 2 t xThese equations can be solved for particular boundary conditions. For a case where a fixedquantity of solute is plated onto a semi–infinite bar (Fig. 1a),Z boundary conditions:C{x, t}dx BandC{x, t 0} 00½ 2¾ xBexpC{x, t} 4DtπDtNow imagine that we create the diffusion couple illustrated in Fig. 1b, by stacking an infiniteset of thin sources on the end of one of the bars. Diffusion can thus be treated by taking awhole set of the exponential functions obtained above, each slightly displaced along the x axis,and summing (integrating) up their individual effects. The integral is in fact the error functionZ x2exp{ u2 }duerf{x} π 0so the solution to the diffusion equation isboundary conditions:C{x 0, t}dx CsC{x, t} Cs (Cs C0 )erf½andx 2 Dt¾C{x, t 0} C0Fig. 1: (a) Thin layer of solute plated on a semi–infinite bar. (b) Two differentsemi–infinite bars.
AH5Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaDiffusivity DataMost metals have similar diffusivities of about 10 12 m2 s 1 at their melting temperatures(Fig. 2). Silicon has the diamond cubic structure with directional bonding which makes theatoms less mobile in spite of the lower density associated with this crystal structure. Interstitialdiffusion is the fastest because of the free availability of interstitial vacancies. Thus, carbonhas about the same activation energy for diffusion as for the self–diffusion of aluminium, buta much larger diffusion coefficient at any temperature (Fig. 2).Fig. 2:Typical self–diffusion coefficients for pure metals and for carbonin ferritic iron. The uppermost diffusivity for each metal is at its meltingtemperature.
AH6Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaThermodynamics of diffusionFick’s first law is empirical in that it assumes a proportionality between the diffusion flux andthe concentration gradient. However, diffusion occurs so as to minimise the free energy. Itshould therefore be driven by a gradient of free energy. But how do we represent the gradientin the free energy of a particular solute?The Chemical PotentialWe first examine equilibrium for an allotropic transition (i.e. when the structure changes butnot the composition). Two phases α and γ are said to be in equilibrium when they have equalfree energies:Gα Gγ(1)FREE ENERGYWhen temperature is a variable, the transition temperature is also fixed by the above equation(Fig. 3).TransitionTemperatureαγTEMPERATUREFig. 3: The transition temperature for an allotropic transformation.A different approach is needed when chemical composition is also a variable. Consider an alloyconsisting of two components A and B. For the phase α, the free energy will in general be afunction of the mole fractions (1 X) and X of A and B respectively:Gα (1 X)µA XµB(2)where µA represents the mean free energy of a mole of A atoms in α. The term µ is called thechemical potential of A, and is illustrated in Fig. 4a. Thus the free energy of a phase is simplythe weighted mean of the free energies of its component atoms. Of course, the latter varieswith concentration according to the slope of the tangent to the free energy curve, as shown inFig. 4.Consider now the coexistence of two phases α and γ in our binary alloy. They will only be inequilibrium with each other if the A atoms in γ have the same free energy as the A atoms inα, and if the same is true for the B atoms:γµαA µAγµαB µBIf the atoms of a particular species have the same free energy in both the phases, then there isno tendency for them to migrate, and the system will be in stable equilibrium if this condition
AH7Materials Science and Metallurgy, 2nd year courseH. K. D. H. Bhadeshiaapplies to all species of atoms. Since the way in which the free energy of a phase varies withconcentration is unique to that phase, the concentration of a particular species of atom neednot be identical in phases which are at equilibrium. Thus, in general we may write:αγγαXA6 XAαγγαXB6 XBwhere Xiαγ describes the mole fraction of element i in phase α which is in equilibrium withphase γ etc.The condition the chemical potential of each species of atom must be the same in all phases atequilibrium is quite general and obviously justifies the common tangent construction illustratedin Fig. 4b.Fig. 4: (a) Diagram illustrating the meaning of a chemical potential µ. (b)The common tangent construction giving the equilibrium compositions of thetwo phases at a fixed temperature.Diffusion in a Chemical Potential GradientThe concept of a chemical potential is powerful indeed. Thus, it is proper to say that diffusion isdriven by gradients of chemical potential (i.e. free energy) rather than chemical concentration:JA MA µA xso thatD A MA µA CA
AH8Materials Science and Metallurgy, 2nd year courseH. K. D. H. Bhadeshiawhere the proportionality constant MA is known as the mobility of A. In this equation, thediffusion coefficient is related to the mobility by comparison with Fick’s first law.The relationship is remarkable: if µA / CA 0 as for the solution illustrated in Fig. 4a,then the diffusion coefficient is positive and the chemical potential gradient is along the samedirection as the concentration gradient. However, if µA / CA 0 then the diffusion will occuragainst a concentration gradient! This can only happen in a solution where the free energycurve has the form illustrated in Fig. 5.A full discussion of the thermodynamics of solutions can be found in Part IA Materials andMinerals Sciences handouts DH9–DH12.Fig. 5: Free energy of mixing plotted as a function of temperature and of theenthalpy HM of mixing. HM 0 corresponds to an ideal solution wherethe atoms of different species always tend to mix at random and it is alwaysthe case that µA / CA 0. When HM 0 the atoms prefer unlikeneighbours and it is always the case that µA / CA 0. When HM 0 the atoms prefer like neighbours so for low temperatures and for certaincomposition ranges µA / CA 0 giving rise to the possibility of uphilldiffusion.
AH9Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaSteady–State SolidificationDuring steady–state solidification the solid/liquid front moves at a constant speed. An observerpositioned at the interface (where x 0) does not see any change in the distribution of soluteahead of the interface (Fig. 6). It follows that any change due to diffusion is compensatedexactly by the fact that the interface is advancing, so thatd2 Cv dC 0dx2D dxwhere v is the solidification front velocity and D the diffusivity in the liquid. A second equationcan be deduced from the fact that the solute flux away from the interface by diffusion mustequal the rate at which solute is partitioned dC (C LS C SL )v Ddx x 0where C SL the concentration in the solid at the interface with the liquid; C LS the concentrationin the liquid at the interface with the solid. Using these two equations to evaluate the twointegration constants yields the concentration C in the liquid as a function of position as:¾½xC C (C C ) exp D/v½¾C (1 k)x C0 0exp kD/vSLLSSLwhere k C0 /C LS since for steady–state solidification C SL C0 .Fig. 6: Concentration profile at the solid–liquid interface during steady–statesolidification. C0 is the average concentration, C SL the concentration in thesolid at the interface with the liquid. C LS the concentration in the liquid atthe interface with the solid. Note that there is a coordinate x which moveswith the interface.
AH10Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaThe Scheil EquationWe assume now that the there is complete mixing in the liquid which has a uniform compositionCL . With reference to Fig. 7, conservation of solute requires that for a fraction f which hassolidified,(C L kC L )df (1 f )dC LZ CLZ fsdfdC L L1 f0C0 C (1 k)so thatC L C0 (1 fs )k 1andC S kC0 (1 fs )k 1This last relation is known as the Scheil Equation.solidliquidconcentrationdfLdCC0SC kCkC00ffraction solidifiedL1Fig. 7: Solidification front moving along one dimension with complete mixingin the liquid. The dashed line represents the distribution of concentration afteran interval of solidification.
AH11Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaConstitutional SupercoolingSolute is partitioned into the liquid ahead of the solidification front. This causes a corresponding variation in the liquidus temperature (the temperature below which freezing begins). Thereis, however, a positive temperature gradient in the liquid, giving rise to a supercooled zone ofliquid ahead of the interface (Fig. 8). This is called constitutional supercooling because it iscaused by composition changes.A small perturbation on the interface will therefore expand into a supercooled liquid. Thisgives rise to dendrites.Fig. 8: Diagram illustrating constitutional supercooling.It follows that a supercooled zone only occurs when the liquidus–temperature (TL ) gradientat the interface is larger than the temperature gradient: TL T T CL i.e.,m x x 0 x x x 0 xwhere m is the magnitude of the slope of the liquidus phase boundary on the phase diagram.From AH8 we note that C LS C SL CL x x 0D/vso that the minimum thermal gradient required for a stable solidification front is TmC0 (1 k)v xkD
AH12Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaHeat Flow During CastingCasting situations may be divided according to whether or not significant thermal gradientsare set up in the solidifying metal. For conducting (metallic) moulds this can be analysed fromthe ratio of the thermal conductance of the interface (h) to that of the casting, termed theBiot number:hLh Bi K/LKwhere K is the thermal conductivity of a casting of length L in the direction of heat flow.Fig. 9: The two different heat transfer situations that arise in casting.For small Bi the thermal resistance of the interface dominates that of the casting, whichtherefore remains at approximately a constant temperature. This is called Newtonian cooling.For this case, the speed v of the solidification front can be obtained by balancing heat evolutionagainst heat extraction:q h T v HFi.e.,v h T HFwhere q is the heat flux and HF is latent heat released on solidification.
AH13Materials Science and Metallurgy, 2nd year courseContinuous Casting of SteelH. K. D. H. Bhadeshia
AH14Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaZener DragRecrystallisation and grain growth involve the movement of grain boundaries. The motion willbe inhibited by second phase particles. The drag on the boundary due to an array of insoluble,incoherent spherical particles is because the grain boundary area decreases when a boundaryintersects the particle. Therefore, to move away from the particle requires the creation of newsurface. The net drag force on a boundary of energy γ per unit area due to a particle of radiusr is given by (Fig. 10)F γ sin{θ} 2πr cos{θ}so that at θ 45 ,Fmax γπrSuppose now that there is a random array of particles, volume fraction f with N particles perunit volume. Only those particles within a distance r can intersect a plane. The number ofparticles intersected by a plane of area 1 m2 will therefore ben 2rN 3f2πr2The drag pressure P is then often expressed asP Fmax n 3γf2rThis may be a significant pressure if the particles are fine.Fig. 10: Zener Drag
AH15Materials Science and Metallurgy, 2nd year courseH. K. D. H. BhadeshiaDiffusion–Controlled GrowthPrecipitates can have a different chemical composition from the matrix. The growth of suchparticles (designated β) is frequently controlled by the diffusion of solute which is partitionedinto the matrix (designated α).As each precipitate grows, so does the extent of its diffusion field. This slows down furthergrowth because the solute has to diffuse over ever larger distances. As we will prove, theparticle size increases with the square root of time, i.e. the growth rate slows down as timeincreases. We will assume in our derivation that the concentration gradient in the matrix isconstant, and that the far–field concentration C0 never changes (i.e. the matrix is semi–infinitenormal to the advancing interface). This is to simplify the mathematics without loosing anyof the insight into the problem.For isothermal transformation, the concentrations at the interface can be obtained from thephase diagram as illustrated below. The diffusion flux of solute towards the interface mustequal the rate at which solute is incorporated in the precipitate so that: CC Cα x D'D 0(Cβ Cα ) t x x{z} {z }rate solute absorbed diffusion flux towards interfaceA second equation can be derived by considering the overall conservation of mass:1(Cβ C0 )x (C0 Cα ) x2On combining these expressions to eliminate x we get:D(C0 Cα )2 x t2x(Cβ Cα )(Cβ C0 )If, as is often the case, Cβ À Cα and Cβ À C0 then¶2 ZµZ Css C0 CαD t so that x '2 x x DtCβ Cα Cαβand1 Cssv'2 CαβrDtwhere v is the velocity. A more precise treatment which avoids the linear profile approximationwould have given:r Css Dv' Cαβt
AH16Materials Science and Metallurgy, 2nd year courseTwinning in Cubic–Close–Packed StructureH. K. D. H. Bhadeshia
Porter and K. E Easterling, Phase Transformations in Metals and Alloys, 2nd edition Chapman and Hall, (1992) [Ln30] 2. A. H. Cottrell, An Introduction to Metallurgy, The Institute of Materials, (1995) [A116] 3. R. W. K. Honeycombe and H. K. D. H. Bhadeshia, Steels, Microstructure and Properties, 2nd edition, Arnold, (1995) [De88] 4. I. J. Polmear, Light Alloys - Metallurgy of the Light Metals .
Heat-Resistant Alloy Castings 8, 9 Aluminum Alloys 9, 10 Aluminum Casting Alloys 10, 11 Copper Alloys 12, 13 Copper Casting Alloys 13, 14 Magnesium Alloys/ Casting Alloys 14 Magnesium Alloys/Wrought Alloys 15 Nickel Alloys 15 Super Alloys 16-18 Tin Alloys 18 Zinc Alloys 19 Precious Metal Alloys 19 Ni-Cr-Mo alloys 19
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 .
Metals vs. Non-Metals; Dot Diagrams; Ions Metals versus Non-Metals Dot Diagrams Metals are on the left side. Non-metals on the right. Metals tend to lose electrons. Non-metals gain them tight. Dot Diagrams (sometimes known as Lewis dot diagrams) are a depiction of an atom’s valence elect
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 .
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 .
Chapter 11 - 18 Ferrous alloys: steels and cast irons Non-ferrous alloys: -- Cu, Al, Ti, and Mg alloys; refractory alloys; and noble metals. Metal fabrication techniques: -- forming, casting, miscellaneous. Hardenability of metals -- measure of ability of a steel to be heat treated. Precipitation hardening
Metals and Non-metals CHAPTER3 In Class IX you have learnt about various elements.You have seen that elements can be classified as metals or non-metals on the basis of their properties. n Think of some uses of metals and non-metals in your daily life. n What properties did you think of while categorising elements a
ASTM Methods. ASTM Listing and Cross References 266-267 Physical Properties 268-269 Sulfur Standards 270-271 PIANO. NEW 272-273 Detailed Hydrocarbon Analysis and SIM DIS 274-275 ASTM Reference Standards 276-303 Diisocyanates298 UOP Standards 304 Miscellaneous: Biocides in Fracking Fluids . NEW. 305 Skinner List, Fire Debris Biofuels 306-309 TPH, Fuels and Hydrocarbons 310-313 Brownfield .
