Materials Engineering & Metallurgy (BPE 402) Lecture Notes PDF

Materials Engineering & Metallurgy (BPE 402) th B.Tech, 5 Semester (Production Engineering)  Module-1 1.1 Introduction of Materials Science and Engineering Materials Science – Investigating relationships that exis...

Materials Engineering & Metallurgy (BPE 402) th B.Tech, 5 Semester (Production Engineering)  Module-1 1.1 Introduction of Materials Science and Engineering Materials Science – Investigating relationships that exist between the structure and properties of materials. Materials Engineering – On the basis of these structure-property correlations, designing or engineering the structure of a material to produce a pre-determined set of properties. Structure Structure of a material usually relates to the arrangement of its internal components. Subatomic - Structure involves electrons within the individual atoms and interactions with their nuclei. Atomic level- structure encompasses the organization of atoms or molecules relative to one another. Microscopic - Which contains large groups of atoms that are normally agglomerated together. Macroscopic – viewable with the naked eye. Property A property is a material trait in terms of the kind and magnitude of response to a specific imposed stimulus. Properties are made independent of material shape and size. Example- A specimen subjected to forces will experience deformation, A polished metal surface will reflect light. Properties of solid materials may be grouped into six different categories: (1) mechanical, (2)electrical, (3) thermal, (4) magnetic, (5) optical and (6) deteriorative. The four components of the discipline of materials science and engineering and their interrelationship. Classification of Materials Solid materials have been conveniently grouped into three basic classifications: (1) metals, (2) ceramics, and (3) polymers. 2 1. Metals- Materials in this group are composed of one or more metallic elements (such as iron, aluminum, copper, titanium, gold, and nickel), and often also nonmetallic elements (for example, carbon, nitrogen, and oxygen) in relatively small amounts. Atoms in metals and their alloys are arranged in a very orderly manner. In comparison to the ceramics and polymers, are relatively dense. Mechanical Property- relatively stiff and strong , ductile (i.e., capable of large amounts of deformation without fracture), and are resistant to fracture. Metallic materials have large numbers of nonlocalized electrons; that is, these electrons are not bound to particular atoms.Many properties of metals are directly attributable to these electrons. Example, metals are extremely good conductors of electricity,and heat, and are not transparent to visible light; a polished metal surface has a lustrous appearance. Some of the metals (viz., Fe, Co, and Ni) have desirable magnetic properties. 2. Ceramics Ceramics are compounds between metallic and nonmetallic elements; they are most frequently oxides, nitrides, and carbides. Examples-aluminum oxide (or alumina, Al2O3), silicon dioxide (or silica, SiO2),silicon carbide (SiC), silicon nitride (Si3N4). Examples of traditional ceramics — clay minerals (i.e., porcelain), cement, and glass. Properties- Relatively stiff and strong—stiffnesses and strengths are comparable to those of the metals , very hard, extremely brittle (lack ductility),.highly susceptible to fracture. Thermal and electrical Properties- Insulative to the passage of heat and electricity low electrical conductivities and are more resistant to high temperatures Optical characteristics-Ceramics may be transparent, translucent, or opaque. Polymers Carbon-based compounds Chain of H-C molecules. Each repeat unit of H-C is a monomer e.g. ethylene (C2H4), Polyethylene – (– CH2 –CH2)n. Polymers include the familiar plastic and rubber materials. Many of them are organic compounds that are chemically based on carbon, hydrogen, and other nonmetallic elements (viz. O, N, and Si). They have very large molecular structures, often chain-like in nature that have a backbone of carbon atoms. Some of the common and familiar polymers are polyethylene (PE), nylon, poly (vinyl chloride)(PVC), polycarbonate (PC), polystyrene (PS), and silicone rubber. 3 Properties Low densities, not as stiff nor as strong as ceramics and metals. Extremely ductile and pliable (i.e., plastic). Relatively inert chemically and unreactive in a large number of environments. Limitations Tendency to soften and/or decompose at modest temperatures, which, in some instances,limits their use. Low electrical conductivities and are nonmagnetic. Composites A composite is composed of two (or more) individual materials, which come from the categories discussed above—viz., metals, ceramics, and polymers. Objective-to achieve a combination of properties that is not displayed by any single material Examples Cemented carbides (WC with Co binder) Plastic molding compounds containing fillers Rubber mixed with carbon black Wood (a natural composite as distinguished from a synthesized composite) Advance Materials Materials that are utilized in high-technology (or high-tech) applications are sometimes termed advanced materials. Examples Include electronic equipment (camcorders, CD/DVD players, etc.), computers, fiber-optic systems, spacecraft, aircraft, and military rocketry, liquid crystal displays (LCDs), and fiber optics. These advanced materials may be typically traditional materials types (e.g., metals, ceramics, polymers) whose properties have been enhanced, and, also newly developed, high-performance materials. Advanced materials include semiconductors, biomaterials, and what we may term“ materials of the future. Biomaterials Biomaterials are employed in components implanted into the human body for replacement of diseased or damaged body parts. These materials must not produce toxic substances and must be compatible with body tissues (i.e., must not cause adverse biological reactions). All of the above materials—metals, ceramics, polymers, composites, and semiconductors—may be used as biomaterials. 4 Example- Titanium and its alloy, Co-Cr alloy, stainless steel, zirconia, HA, TiO2 etc. Semiconductors Semiconductors have electrical properties that are intermediate between the electrical conductors (viz. metals and metal alloys) and insulators (viz. ceramics and polymers). The electrical characteristics of these materials are extremely sensitive to the presence of minute concentrations of impurity atoms, for which the concentrations may be controlled over very small spatial regions. Semiconductors have made possible the advent of integrated circuitry that has totally revolutionized the electronics and computer industries (not to mention our lives) over the past three decades. The Materials Selection Process Pick Application and determine required Properties. Properties: mechanical, electrical, thermal, magnetic, optical, deteriorative. Properties- Identify candidate Material(s) Material: structure, composition. Material- Identify required Processing Processing: changes structure and overall shape Example: casting, sintering, vapor deposition, doping forming, joining, annealing. 1.2 Defects in Solids The term “defect” or “imperfection” is generally used to describe any deviation from the perfect periodic array of atoms in the crystal. The properties of some materials are extremely influenced by the presence of imperfections such as mechanical strength, ductility, crystal growth, magnetic hysteresis, dielectric strength, condition in semiconductors, which are termed structure sensitive are greatly affected by the-relatively minor changes in crystal structure caused by defects or imperfections. There are some properties of materials such as stiffness, density and electrical conductivity which are termed structure-insensitive, are not affected by the presence of defects in crystals. It is important to have knowledge about the types of imperfections that exist and the roles they play in affecting the behavior of materials. Crystal imperfections can be classified on the basis of their geometry as 5 Point Defects in Metals It is a zero dimension defect, associated with one or two atomic positions. Vacancies -The simplest of the point defects is a vacancy, or vacant lattice site, one normally occupied from which an atom is missing. All crystalline solids contain vacancies and, in fact, it is not possible to create such a material that is free of these defects, vacant atomic sites in a structure. Self-Interstitials- when an atom occupies an interstitial site where no atom would ordinarily appear, causing an interstitialcy. 6 Point Defects in Ceramics Vacancies- vacancies exist in ceramics for both cations and anions. Interstitials - interstitials exist for cations, interstitials are not normally observed for anions because anions are large relative to the interstitial sites. Frenkel Defect To maintain the charge neutrality, a cation vacancy-cation interstitial pair occur together. This is called a Frenkel defect. The cation leaves its normal position and moves to the interstitial site. There is no change in charge because the cation maintains the same positive charge as an interstitial. Schottky Defect A cation vacancy–anion vacancy pair known as a Schottky defect. To maintain the charge neutrality, remove one cation and one anion; this creates two vacancies. 7 The equilibrium number of vacancies for a given quantity of material depends on and increases with temperature according to Equilibrium concentration varies with temperature Where, N is the total number of atomic sites, Qv is the energy required for the formation of a vacancy, T is the absolute temperature in kelvins, and k is the gas or Boltzmann’s constant. 1.38 x 10-23 J/atom-K. Equilibrium Concentration: 1. Find the equilibrium concentration of vacancies in aluminium and nickel at 0K,300 K and 900K. Given ∆Hf= 68 ×103 KJ/mol. Solution- (i) at 0K (ii) at 300 K 2. Calculate the equilibrium number of vacancies per cubic meter for copper at 1000oC. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000oC) for copper are 63.5 g/mol and 8.4 g/cm3, respectively. Solution- The value of N, the number of atomic sites per cubic meter for copper, from its atomic weight its density and Avogadro’s number according to 8  =8.0 1028 atoms/m3 Thus, the number of vacancies at 1000oC (1273K) is equal to = 2.2 ×1025 vacancies/m3 EFFECT OF POINT IMPERFECTIONS The presence of a point imperfection introduces distortions in the crystal. In the case of impurity atom, because of its difference in size, elastic strains are created in the regions surrounding the impurity atom. All these factors tend to increase the potential energy of the crystal called ‘enthalpy’. The work done for the creation of such a point defect is called the ‘enthalpy of formation’ of the point imperfection LINE IMPERFECTIONS A dislocation is a linear or one-dimensional defect around which some of the atoms are misaligned. The defects, which take place due to distortion of atoms along a line, in some direction are called as ‘line defects,.Line defects are also called dislocations. It is responsible for the phenomenon of slip by which most metals deform plastically. The two types of dislocations are, Edge dislocation It is a linear defect that centers around the line that is defined along the end of the extra half-plane of atoms. The distorted configuration extends all along the edge into the crystal. Thus as the region of maximum distortion is centered around the edge of the incomplete plane, this distortion represents a line imperfection and is called an edge dislocation. Edge dislocations are represented by ‘⊥’ or ‘Τ‘ depending on whether the incomplete plane starts from the top or from the bottom of the crystal. These two configurations are referred to as positive and negative edge dislocations respectively. 9 Screw dislocation:- In this dislocation, the atoms are displaced in two separate planes perpendicular to each other. It forms a spiral ramp around the dislocation. The Burgers Vector is parallel to the screw dislocation line. Speed of movement of a screw dislocation is lesser compared to edge dislocation. Burgers vector - The magnitude and direction of the lattice distortion associated with a dislocation is expressed in terms of a Burgers vector, denoted by a b. The Burger vector can be found by the gap in the Burger circuit which is obtained by moving equal distances in each direction around the dislocation. 10 Mixed dislocations - Most dislocations found in crystalline materials are probably neither pure edge nor pure screw, but exhibit components of both types; these are termed mixed dislocations. Surface imperfections Surface imperfections arise from a change in the stacking of atomic planes on or across a boundary. The change may be one of the orientations or of the stacking sequence of atomic planes. In geometric concept, surface imperfections are two- dimensional. They are of two types external and internal surface imperfections. External Surfaces They are the imperfections represented by a boundary. At the boundary the atomic bonds are terminated. Surface atoms are not bonded to the maximum number of nearest neighbors, and are therefore in a higher energy state than the atoms at interior positions. The bonds of these surface atoms that are not satisfied give rise to a surface energy, expressed in units of energy per unit area (J/m2 or erg/cm2). Grain Boundaries The boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials. 11 Twin Boundaries A twin boundary is a special type of grain boundary across which there is a specific mirror lattice symmetry; that is, atoms on one side of the boundary are located in mirror-image positions of the atoms on the other side. The region of material between these boundaries is appropriately termed a twin. Twins result from atomic displacements that are produced from applied mechanical shear forces (mechanical twins), and also during annealing heat treatments following deformation (annealing twins). Volume Defects- These include pores, cracks, foreign inclusions, and other phases. They are normally introduced during processing and fabrication steps. Effect on property There are some properties of materials such as stiffness, density and electrical conductivity which are termed structure-insensitive, are not affected by the presence of defects in crystals while there are many properties of greatest technical importance such as mechanical strength, ductility, crystal growth, magnetic. Hysteresis, dielectric strength, condition in semiconductors, which are termed structure sensitive are greatly affected by the-relatively minor changes in crystal structure caused by defects or imperfections. 1.3 Diffusion in solids Diffusion is a process of mass transport by atomic movement under the influence of thermal energy and a concentration gradient. Atoms move from higher to lower concentration region. 12 Figure 1. (a) A copper–nickel diffusion couple after a high-temperature heat treatment, showing the alloyed diffusion zone. (b) Schematic representations of Cu (red circles) and Ni (blue circles) atom locations within the couple. (c) Concentrations of copper and nickel as a function of position across the couple. Figure 1 shows, pure copper and nickel at the two extremities of the couple, separated by an alloyed region. Concentrations of both metals vary with position as shown in Figure1(c). This result indicates that copper atoms have migrated or diffused into the nickel, and that nickel has diffused into copper. Diffusion Mechanisms Diffusion is just the stepwise migration of atoms from lattice site to lattice site. In fact, the atoms in solid materials are in constant motion. For an atom to make such a move, two conditions must be met: (1) there must be an empty adjacent site, and (2) the atom must have sufficient energy to break bonds with its neighbor atoms and then cause some lattice distortion during the displacement. Vacancy Diffusion In this mechanism involves the interchange of an atom from a normal lattice position to an adjacent vacant lattice site or vacancy. This process necessitates the presence of vacancies, and the extent to which vacancy diffusion can occur is a function of the number of these defects that are present. Diffusing atoms and vacancies exchange positions, the diffusion of atoms in one direction corresponds to the motion of vacancies in the opposite direction. Both self-diffusion and inter-diffusion occur by this mechanism. 13 Interstitial Diffusion In this diffusion involves atoms that migrate from an interstitial position to a neighboring one that is empty. This mechanism is found for inter-diffusion of impurities such as hydrogen, carbon, nitrogen, and oxygen, which have atoms that are small enough to fit into the interstitial positions. In most metal alloys, interstitial diffusion occurs much more rapidly than diffusion by the vacancy mode, since the interstitial atoms are smaller and thus more mobile. 14 Steady-state diffusion Steady-state diffusion is the situation when the diffusion flux is independent of time. Fick’s first law describes steady-state diffusion and is given by Where, J is the diffusion flux or the mass transported per unit time per unit area and dC/dx is the concentration gradient. D is known as the diffusion coefficient The negative sign in this expression indicates that the direction of diffusion is down the concentration gradient, from a high to a low concentration Example- Diffusion of atoms of a gas through a plate of metal for which the concentrations (or pressures) of the diffusing species on both surfaces of the plate are held constant. 15 Non-steady-state diffusion Most practical diffusion situations are non steady-state ones. In this the diffusion flux and the concentration gradient at some particular point in a solid vary with time, with a net accumulation or depletion of the diffusing species resulting. This is described by Fick’s second law A solution to this equation can be obtained for a semi-infinite solid with the following boundary conditions For t=0, C = C0 at 0 ≤ x ≤ ∞ For t > 0, C= Cs at x=0 C=C0 at x=∞ Application of these boundary conditions to Equation 1 yields the solution Factors affecting Diffusion Diffusing species The magnitude of the diffusion coefficient D is indicative of the rate at which atoms diffuse. Coefficients, both self- and inter-diffusion. The diffusing species as well as the host material influence the diffusion coefficient. As the value of D is fixed for a given element in a given material, the extent of diffusion is first decided by the diffusing species itself.. 16 Temperature Temperature is the most important factor, which influence on the coefficients and diffusion rates. Temperature dependence of the diffusion coefficient is expresses as Where, Do is the pre-exponential factor, Qd is the activation energy for diffusion, T is absolute temperature in kelvin and R is gas constant. Mechanisms/modes of plastic deformation Plastic deformation in crystalline solid is accomplished by means of various processes mentioned below; among which slip is the most important mechanism. Plastic deformation of crystalline materials takes place by mechanisms which are very different from that for amorphous materials (glasses). Plastic deformation in amorphous materials occur by other mechanisms including flow (~viscous fluid) and shear banding. Plastic deformation by dislocation Motion (SLIP)  SLIP is the most important mechanism of plastic deformation. At low temperatures (especially in BCC metals) twinning may also become important.  At the fundamental level plastic deformation (in crystalline materials) by slip involves the motion of dislocations on the slip plane (creating a step of Burgers vector).  Slip is caused by shear stresses (at the level of the slip plane). Hence, a purely hydrostatic state of stress cannot cause slip.  A slip system consists of a slip direction lying on a slip plane.  Slip is analogous to the mode of locomotion employed by a caterpillar    Dislocations move more easily on specific planes and in specific directions.  Ordinarily, there is a preferred plane (slip plane), and specific directions (slip direction) along which dislocations move. The combination of slip plane and slip direction is called the slip system.  The slip system depends on the crystal structure of the metal.  The slip plane is the plane that has the most dense atomic packing (the greatest planar density). The slip direction is most closely packed with atoms (highest linear density).  In CCP, HCP materials the slip system consists of a close packed direction on a close packed plane.  Just the existence of a slip system does not guarantee slip → slip is competing against other processes like twinning and fracture. If the stress to cause slip is very high (i.e. CRSS is very high), then fracture may occur before slip (like in brittle ceramics). 17   For slip to occur in polycrystalline materials, 5 independent slip systems are required. Hence, materials which are ductile in single crystalline form may not be ductile in polycrystalline form. CCP crystals (Cu, Al, and Au) have excellent ductility.  At higher temperatures more slip systems may become active and hence polycrystalline materials which are brittle at low temperature may become ductile at high temperature. Crystal Slip plane(s) Slip direction Number of slip systems FCC {111} ½ 12 HCP (0001) 3 BCC {110}, {112}, {123} ½ 48 {110} NaCl (Ionic) ½ 6 {111} not a slip plane C (Diamond cubic) {111} ½ 12 TiO2(Rutile) {101} CaF2, UO2, ThO2 {001} Fluorite CsCl {110} NaCl, LiF, MgO {110} 6 Rock Salt C, Ge, Si {111} 12 Diamond cubic MgAl2O4 {111} Spinel Al2O3 (0001) Hexagonal Slip in Single Crystal If a single crystal of a metal is stressed in tension beyond its elastic limit, it elongates slightly and a step appears on the surface due to the relative displacement of one part of the crystal with respect to the others and the elongation stops. 18  Further increase in the load causes movement of another parallel plane, resulting in another step. Similarly numbers of small steps are formed on the surface of the single crystal that are parallel to one another and loop around the circumference of the specimen. Each step (shear band) results from the movement of a large number of dislocations and their propagation in the slip system. Extent of slip in a single crystal depends on the magnitude of shearing stress produced by external loads, geometry of the crystal structure and the orientation of he active slip planes with respect to the shearing stress. Slip begins when the shearing stress on slip plane in the slip direction/Resolved Shear Stress (RSS) reaches a critical value called the Critical Resolved Shear Stress (CRSS) and plastic deformation starts (The actual Schmid’s law) Even if we apply an tensile force on the specimen → the shear stress resolved onto the slip plane is responsible for slip. 19  τ RSS is maximum (P/2A) when ϕ = λ=45o If the tension axis is normal to slip plane i.e. λ=90o or if it is parallel to the slip plane i.e. ϕ = 90o then τ RSS = 0 and slip will not occur as per Schmid’s law. τCRSS is a material parameter, which is determined from experiments. Problem Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a direction. (a) Compute the resolved shear stress along a (110) plane and in a direction when a tensile stress of 52 MPa (7500 psi) is applied − (b) If slip occurs on a (110) plane and in a direction, and the critical resolved shear stress is 30 MPa (4350 psi), calculate the magnitude of the applied tensile stress necessary to initiate yielding. 20 Solution Determine the value of ,the angle between the normal to the (110) slip plane (i.e., the direction) and the direction using [u1v1w1] = , [u2v2w2] = and the following equation. − Similarly determine the value of λ, the angle between and directions as follows:  (−1)(0) + (1)(1) + (1)(0)  λ = cos −1   = cos −1 ( 1 ) = 54.7 o  [(−1) + (1) + (1) ][(0) + (1) + (0)  2 2 2 2 2 2 ]  3 Then calculate the value of τ RSS using the following expression Yield Strength σY 30 MPa σy = = 73.4 Mpa (cos 45)(cos 54.7) Plastic deformation by Twin In addition to slip (dislocation movement), plastic deformation can also occur by twinning. 21  Twinning results when a portion of the crystal takes up an orientation that is related to the orientation of the rest of the un twinned lattice in a definite, symmetrical way. Twinned portion of the crystal is a mirror image of the parent crystal and the plane of symmetry between the two portions is called twinning plane. Twinning may favorably reorient slip systems to promote dislocation movement. Twins are generally of two types: Mechanical Twins and Annealing twins Mechanical twins are generally seen in bcc or hcp metals and produced under conditions of rapid rate of loading and decreased temperature. Annealing twins are produced as the result of annealing. These twins are generally seen in fcc metals. Annealing twins are usually broader and with straighter sides than mechanical twins. 22 (a) Mechanical Twins (Neumann bands in iron), (b) Mechanical Twins in zinc produced by polishing (c) Annealing Twins in gold-silver alloy Twinning generally occurs when the slip systems are restricted or when the slip systems are restricted or when something increases the critical resolved shear stress so that the twinning stress is lower than the stress for slip. So, twinning generally occurs at low temperatures or high strain rates in bcc or fcc metals or in hcp metals. Twinning occurs on specific twinning planes and twinning directions. 23 Bauschinger effect The Bauschinger effect refers to a property of materials where the material's stress/strain characteristics change as a result of the microscopic stress distribution of the material. For example, an increase in tensile yield strength occurs at the expense of compressive yield strength. The effect is named after German engineer Johann Bauschinger. The Bauschinger effect is normally associated with conditions where the yield strength of a metal decreases when the direction of strain is changed. It is a general phenomenon found in most polycrystalline metals. The basic mechanism for the Bauschinger effect is related to the dislocation structure in the cold worked metal. As deformation occurs, the dislocations will accumulate at barriers and produce dislocation pile- ups and tangles. Based on the cold work structure, two types of mechanisms are generally used to explain the Bauschinger effect. Work Hardening Room temperature deformation. Common forming techniques used to change the cross sectional area: 24 Dislocations during Cold Work Dislocations entangle one another during cold work. Dislocation motion becomes more difficult, which makes the material stronger overall Isotropic grains are approx. spherical, Anisotropic (directional) since rolling equiaxed & randomly oriented. affects grain orientation and shape. Result of Cold Work Dislocation density increases, which leads to a increase in yield strength: Materials becomes harder. Ductility and tensile strength also increases. Recovery, Recrystallization & Grain Growth Recovery Recovery takes place at low temperatures of annealing. Apparently no change in microstructure. During recovery, some of the stored internal strain energy is relieved through dislocation motion due to enhanced atomic diffusion at the elevated temperatures. 25  Leads to reduction in the number of dislocations. This process also removes the residual stresses formed due to cold working significant. The recovering of physical and mechanical properties varies with the temperature and time. Recovery is a relaxation process with the following characteristics:  There is no incubation period  Recovery rate is large at the beginning, and then it slows down till it is near zero  Recovery has a limit value varying with temperature; the higher the temperature, the greater is the limit value and the shorter is the time needed to reach the limit value  The greater the deformation, the greater is the initial recovery rate, and decrease in grain size helps to accelerate the recovery process The characteristic of recovery can be expressed as the following equation: Where t is the time of heating under constant temperature x is the fraction of property increase caused by cold work after heating c is a constant related with material and temperature The value of constant parameter c can be described with the Arrhenius equation: Recrystallization After recovery is complete, the grains are still in a relatively high strain energy state. Recrystallization is the formation of a new set of strain-free and uniaxial grains that have low dislocation densities. The temperature at which materials are recrystallized is known as the recrystallization temperature, Trecrystallization ∈ (0.3 – 0.5) Tm The driving force to produce the new grain structure is the internal energy difference between strained and unstrained material. The new grains form as very small nuclei and grow until they consume the parent material. Recrystallization is a heterogeneous process and dependent on the deformation state of steels. The kinetics of recrystallization depends on nucleation rate, N, and growth rate, G. Grain Growth After recrystallization, the strain-free grains will continue to grow if the metal specimen is left at elevated temperatures. Grains begin to grow via grain boundary immigration; this phenomenon is called grain growth. 26  Grain growth is driven by the tendency to decrease the total boundary surface energy by decreasing the grain boundary area. Large grains grow at the expense of smaller grains. (a) (b) (c) (d) Fig.1.1. (a) Work hardening, (b) recovery, (c) recrystallization, and (d) grain growth during annealing. 1. Callister's Materials Science and Engineering William D Callister (Adapted by R. Balasubramaniam) Wiley Inida (P) Ltd., 2007. 27  Module 2 and 3 Solidification Solidification is basically phase transformation from liquid phase to solid phase. The progress of a phase transformation takes place in two stages: nucleation and growth. Nucleation involves the appearance of very small particles, or nuclei of the new phase (often consisting of only a few hundred atoms), which are capable of growing. During the growth stage these nuclei increase in size, which results in the disappearance of some (or all) of the parent phase. Cooling Curve Driving Force Solidification is undoubtedly the most important processing route for metals and alloys. Consider a pure metal (Fig. 1). At the fusion temperature Tf, ΔG = 0 so that ΔGf = ΔHf− TfΔSf = 0 or ΔHf = TfΔSf where ΔHf is the latent heat of fusion, ΔGf is the Gibb’s free energy and ΔSf is the entropy,i.e positive for melting.For any temperature T, ΔG = ΔH − TΔS Or ΔG ≅ ΔHf − TΔSf = ΔSf (Tf− T) = ΔSf ΔT Where ΔT is undercooling. 28 Fig.1 Driving Force for nucleation. The driving force is therefore proportional to the undercooling provided that the latent heat and the entropy of fusion do not vary much with temperature. Nucleation There are two types of nucleation: homogeneous and heterogeneous.The distinction between them is made according to the site at which nucleating events occur. For the homogeneous type, nuclei of the new phase form uniformly throughout the parent phase, whereas for the heterogeneous type, nuclei form preferentially at structural in homogeneities, such as container surfaces, insoluble impurities, grain boundaries, dislocations, and so on. Homogeneous Nucleation Nucleation without preferential nucleation sites is homogeneous nucleation.Homogeneous nucleation occurs spontaneously and randomly, but it requires Superheating or supercooling of the medium. Let us first consider the solidification of a pure material, assuming that nuclei of the solid phase form in the interior of the liquid as atoms cluster together so as to form a packing arrangement similar to that found in the solid phase. Furthermore, it will be assumed that each nucleus is spherical in geometry and has a radius r. Fig.2 Schematic diagram showing the There are two contributions to the total free energy change that accompany a solidification transformation. (i)The first is the free energy difference between the solid and liquid phases, or the volume free energy, i.e. where is the volume free energy change. (ii)The second is the surface energy, results from the formation of the nucleation of a spherical solid particle in a liquid, i.e Finally, the total free energy change is equal to the sum of these two contributions—that is 29  …..(1) Critical Radius(r*)- Differentiate the equation (Equation 1) with respect to r, set the resulting expression equal to zero, and then solve for critical radius ( r*). That is and activation free energy (∆G*) = When radius (r) is less than critical radius ( r*),termed as an embryo. and when radius (r) is greater than critical radius ( r*),termed as an nuclei. Heterogeneous nucleation Heterogeneous nucleation forms at preferential sites such as phase boundaries, surfaces (of container, bottles, etc.) or impurities like dust. At such preferential sites, the effective surface energy is lower, thus diminishes the free energy barrier and facilitating nucleation. Heterogeneous nucleation occurs much more often than homogeneous nucleation. Let us consider the nucleation, on a flat surface, of a solid particle from a liquid phase. It is assumed that both the liquid and solid phases “wet” this flat surface, that is, both of these phases spread out and cover the surface. Taking a surface tension force balance in the plane of the flat surface leads to the following expression: 30  where, γIL , γSI and γSL is the interfacial energy between interface- liquid, solid –interface and solid –liquid respectively. And θ is the contact angle. Where S(θ) is the function of contact angle θ as follows: Geometry of Solidification The chill zone contains fine crystals nucleated at the mould surface. There is then selective growth into the liquid as heat is extracted from the mould. If the liquid in the centre of the mould is undercooled sufficiently there may also be equiaxed grains forming. 31  Phase Diagram Introduction Phase diagrams are an important tool in the armory of an materials scientist In the simplest sense a phase diagram demarcates regions of existence of various phases. (Phase diagrams are maps) Phase diagrams are also referred to as “equilibrium diagrams” or “constitutional diagrams”. This usage requires special attention: through the term used is “equilibrium”, in practical terms the equilibrium is not global equilibrium but Microstructural level equilibrium. → those involving time and those which do Broadly two kinds of phase diagrams can be differentiated* not involve time. In this chapter we shall deal with the phase diagrams not involving time. o This type can be further sub classified into: o Those with composition as a variable (e.g. T vs. %Composition) o Those without composition as a variable (e.g. P vs. T) Time-Temperature-Transformation (TTT) diagrams and Continuous-Cooling-Transformation (CCT) diagrams involve time. Components of a system Independent chemical species which comprise the system. These could be Elements, Ions, Compounds Example: Au-Cu system : Components →Au, Cu (elements) Ice-water system : Component→H2O (compound) Al2O3-Cr2O3 system : Components→Al2O3, Cr2O3 Phase A physically homogeneous and distinct portion of a material system (e.g. gas, crystal, amorphous…) Gases : Gaseous state always a single phase → mixed at atomic or molecule level. → e.g. Nacl in H 2O and Liquid mixtures consists of two or Liquids: Liquid solution is a single phase more phases → e.g. Oil in water (no mixing at the atomic level) Solids: In general due to several compositions and crystals structures many phases are possible. 32  o For the same composition different crystal structures represent different phases. E.g. Fe (BCC) and Fe (FCC) are different phases What kinds of phases exist? Based on state → Gas, Liquid, Solid Based on atomic order → Amorphous, Quasi-crystalline, Crystalline Based on band structure → Insulating, Semi-conducting, Semi-metallic, Metallic Based on Property → Para-electric, Ferromagnetic, Superconducting Based on stability → Stable, Metastable, Unstable Also sometimes- Based on size/geometry of an entity → Nanocrystalline, mesoporous, layered. Phase transformation Phase transformation is the change of one phase into another. For example  Water → Ice and α-Fe (BCC) → γ-Fe (FCC) Grain The single crystalline part of polycrystalline metal separated by similar entities by a grain boundary Solute The component of either a liquid or solid solution that is present to a lesser or minor extent; the component that is dissolved in the solvent. Solvent The component of either a liquid or solid solution that is present to a greater or major extent; the component that dissolves the solute. System System has two meanings. First, ‘‘system’’ may refer to a specific body of material or object. Or, it may relate to the series of possible alloys consisting of the same components, but without regard to alloy composition. Solubility Limit For many alloy systems and at some specific temperature, there is a maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution; this is called a Solubility Limit. Microstructure (Phases + defects + residual stress) & their distributions 33  Structures requiring magnifications in the region of 100 to 1000 times. (or) The distribution of phases and defects in a material. Phase diagram Map that gives relationship between phases in equilibrium in a system as a function of T, P and composition. Map demarcating regions of stability of various phases Variables/Axis of phase diagrams The axes can be: o Thermodynamic (T, P, V) o Kinetic (t) or Composition variables (C, %X) In single component systems (unary systems) the usual variables are T & P In phase diagrams used in materials science the usual variable are T & %X In the study of phase transformation kinetics TTT diagrams or CCT diagrams are also used where the axis are T & t System Components Phase diagrams and the systems they describe are often classified and named for the number (in Latin) of components in the system: Number of components Name of system or diagram One Unary Two Binary Three Ternary Four Quaternary Five Quinary Six Sexinary Seven Septenary Eight Octanary Nine Nonary Ten Decinary Experimental Methods Thermal Analysis: A plot is made of temperature vs. time, at constant composition, the resulting cooling curve will show a change in slope when a phase change occurs because of the evolution of heat by the phase change. This method seems to be best for determining the initial and final temperature of solidification. Phase changes occurring solely in the solid state generally involve only small heat changes, and other methods give more accurate results. 34 Metallographic Methods: This method consists in heating samples of an alloy to different temperatures, waiting for equilibrium to be established, and then quickly cooling to retain their high temperature structure. The samples are then examined microscopically. This method is difficulty to apply to metals at high temperatures because the rapidly cooled samples do not always retain their high temperature structure, and considerable skill is then required to interpret the observed microstructure correctly. X-ray diffraction: Since this method measures lattice dimensions, it will indicate the appearance of a new phase either by the change in lattice dimension or by the appearance of a new crystal structure. This method is simple, precise, and very useful in determining the changes in solid solubility with temperature. Gibbs Phase Rule The phase rule connects the Degrees of Freedom, the number of components in a system and the number of phases present in a system via a simple equation. To understand the phase rule one must understand the variables in the system along with the degrees of freedom. We start with a general definition of the phrase “degrees of freedom”. Degrees of Freedom: The degree of freedom, F, are those externally controllable conditions of temperature, pressure, and composition, which are independently variable and which must be specified in order to completely define the equilibrium state of the system. The degrees of freedom cannot be less than zero so that we have an upper limit to the number of phases that can exist in equilibrium for a given system. Variables in a phase diagram C – No. of components P – No. of phases F – No. of degrees of freedom Variables in the system = Composition variables + Thermodynamic variables Composition of a phase specified by (C – 1) variables (If the composition is expressed in %ages then the total is 100% → there is one equation connecting the composition variables and we need to specify only (C - 1) composition variables) No. of variables required to specify the composition of all phases: P(C – 1) (as there are P phases and each phase needs the specification of (C – 1) variables) 35  Thermodynamic variables = P + T (usually considered) = 2 (at constant pressure (e.g. atmospheric pressure) the thermodynamic variable becomes 1) Total no. of variables in the system = P (C – 1) + 2 F < no. of variables → F < P (C – 1) + 2For a system in equilibrium the chemical potential of each species is same in all the phases If α, β, γ… are phases, then: μA (α) = μA (β) = μA (γ)….. Suppose there are 2 phases (α and β phases) and 3 components (A, B, C) in each phase then : μA(α) = μA(β), μB(α) = μB(β), μC(α) = μC(β) → i.e. there are three equations. For each component there are (P – 1) equations and for C components the total number of equations is C(P – 1). In the above example the number of equations is 3(2 – 1) = 3 equations. F = (Total number of variables) – (number of relations between variables) = [P(C – 1) + 2] – [C(P – 1)] = C – P + 2 In a single phase system F = Number of variables P↑ → F↓ (For a system with fixed number of components as the number phases increases the degrees of freedom decreases. Unary Phase Diagram Let us start with the simplest system possible: the unary system wherein there is just one component. Though there are many possibilities even in unary phase diagram (in terms of the axis and phases), we shall only consider a T-P unary phase diagram. Let us consider the water (H2O) unary phase diagram The Gibbs phase rule here is: F=C-P+2 (2 is for T&P) (no composition variables here) Along the 2 phase co-existence (at B & C) lines the degree of freedom (F) is 1→ i.e. we can chose either T or P and the other will be automatically fixed. The 3 phase co-existence points (at A) are invariant points with F=0. (Invariant point implies they are fixed for a given system). The single phase region at point D, T and P can both be varied while still being in the single phase region with F = 2. 36  The above figure represents the phase diagram for pure iron. The triple point temperature and pressure are 490ºC and 110 kbars, respectively. α, γ and ε refer to ferrite, austenite and ε-iron, respectively. δ is simply the higher temperature designation of α. Binary Phase Diagram  Binary implies that there are two components.  Pressure changes often have little effect on the equilibrium of solid phases (unless of course we apply ‘huge’ pressures).  Hence, binary phase diagrams are usually drawn at 1 atmosphere pressure.  The Gibbs phase rule is reduced to:  Variables are reduced to : F = C – P + 1 (1 is for T).  T & Composition (these are the usual variables in materials phase diagrams)  In the next page we consider the possible binary phase diagrams. These have been classified based on:  Complete solubility in both liquid & solid states  Complete solubility in both liquid state, but limited solubility in the solid state  Limited solubility in both liquid & solid states 37 Isomorphous Phase Diagram Isomorphous phase diagrams form when there is complete solid and liquid solubility. Complete solid solubility implies that the crystal structure of the two components have to be same and Hume-Rothery rules to be followed. Examples of systems forming isomorphous systems: Cu-Ni, Ag-Au, Ge-Si, Al2O3-Cr2O3 Both the liquid and solid contain the components A and B. In binary phase diagrams between two single phase regions there will be a two phase region → In the isomorphous diagram between the liquid and solid state there is the (Liquid + Solid) state. The Liquid + Solid state is NOT a semi-solid state → it is a solid of fixed compositio n and structure, in equilibrium with a liquid of fixed composition. In some systems (e.g. Au-Ni system) there might be phase separation in the solid state (i.e.,the → these will be considered as a complete solid solubility criterion may not be followed) variation of the isomorphous system (with complete solubility in the solid and the liquid state. 38 Cooling curves: Isomorphous system Isomorphous Phase Diagram 39 Tie line and Lever rule Chemical Composition of Phases: To determine the actual chemical composition of the phases of an alloy, in equilibrium at any specified temperature in a two phase region, draw a horizontal temperature line, called a tie line, to the boundaries of the field. These points of intersection are dropped to the base line, and the composition is read directly. Relative Amounts of Each Phase: To determine the relative amounts of the two phases in equilibrium at any specified temperature in a two phase region, draw a vertical line representing the alloy and a horizontal temperature line to the boundaries of the field. The vertical line will divide the horizontal line into two parts whose lengths are inversely proportional to the amount of the phases present. This is also known as Lever rule. The point where the vertical line intersects the horizontal line may be considered as the fulcrum of a lever system. The relative lengths of the lever arms multiplied by the amounts of the phases present must balance. Tie line and Lever rule We draw a horizontal line (called the Tie Line)at the temperature of interest (say T0). Let Tie line is XY. Solid (crystal) of composition C 1 coexists with liquid of composition C 2 Note that tie lines can be drawn only in the two phase coexistence regions (fields). Though they may be extended to mark the temperature. To find the fractions of solid and liquid we use the lever rule. The portion of the horizontal line in the two phase region is akin to ‘lever’ with the fulcrum at the nominal composition (C0) The opposite arms of the lever are proportional to the fraction of the solid and liquid phase present (this is lever rule). 40 Variations of Isomorphous System An alloy typically melts over a range of temperatures. However, there are special compositions which can melt at a single temperature like a pure metal. There is no difference in the liquid and solid composition. It begins and ends solidification at a constant temperature with no change in composition, and its cooling curve will show a horizontal line. Such alloys are known as a congruent-melting alloys, sometimes known as a pseudo- eutectic alloy. Ex: Cu-Au, Ni-Pd.  Congruently melting alloys → just like a pure metal  Is the DOF 1? No: in requiring that we have exhausted the degree of freedom. Hence T is automatically fixed → DOF is actually Zero..! 41 Variations of Isomorphous System Elevation in the MP means that the solid state is ‘more stable’ (crudely speaking the ordered state is more stable) → ordering reaction is seen at low T. Depression in MP ‘means’ the liquid state (disordered) is more stable→ phase separation is seen at low T. (phase separation can be thought of as the opposite of ordering. Ordering (compound formation) occurs for –ve values for ΔH mix). Equilibrium Cooling Figure: The above figure represents the very slow cooling, under equilibrium conditions, of a particular alloy 70A-30B will now be studied to observe the phase changes that occur This alloy at temperature T0 is a homogeneous single-phase liquid solution (a) and remains so until temperature T1is reached. Since T1is on the liquidus line, freezing or solidification now begins. 42  The first nuclei of solid solution to form α1 will be very rich in the higher melting point metal A and will be composed of 95A-5B (by tie line rule). Since the solid solution in forming takes material very rich in A from the liquid, the liquid must get richer in B. Just after the start of solidification, the composition of the liquid is approximated as 69A-31B (b). When the lower temperature T2 is reached, the liquid composition is at L2. The only solid solution in equilibrium with L2 and therefore the only solid solution forming at T2 is α2. Applying tie line rule, α2 is composed of 10B. Hence, as the temperature is decreased, not only does the liquid composition become richer in B but also the solid solution. At T2 ,crystals of α2 are formed surrounding the α1 composition cores and also separate dendrites of αz (see figure in below). In order for equilibrium to be established at T2, the entire solid phase must be a composition α2. This requires diffusion of B atoms to the A-rich core not only from the solid just formed but also from the liquid. This is possible in crystal growth (c). The composition of the solid solution follows the solidus line while the composition of liquid follows the liquidus line, and both phases are becoming richer in B. At T3 (d), the solid solution will make up approximately three-fourths of all the material present. Finally, the solidus line is reached at T4, and the last liquid L4, very rich in B, solidifies primarily at the grain boundaries (e). However, diffusion will take place and all the solid solution will be of uniform composition α(70A- 30B), which is the overall composition of the alloy (f). There are only grains and grain boundaries. There is no evidence of any difference in chemical composition inside the grains, indicating that diffusion has made the grain homogeneous. 43  Non Equilibrium Cooling - Coring  In actual practice it is extremely difficult to cool under equilibrium conditions. Since diffusion in the solid state takes place at a very slow rate, it is expected that with ordinary cooling rates there will be some difference in the conditions as indicated by the equilibrium diagram.  Consider again 70A-30B alloy, solidification starts at T1 forming a solid solution of composition α1.  At T2 the liquid is L2 and the solid solution now forming is of composition α2. Since diffusion is too slow to keep pace with crystal growth, not enough time will be allowed to achieve uniformity in the solid, and the average composition will be between α1 and α2, say α’2.  As the temperature drops, the average composition of the solid solution will depart still further from equilibrium conditions. It seems that the composition of the solid solution is following a “nonequilibrium” solidus line α1 to α’5, shown dotted lines in figure.  The liquid, on the other hand, has essentially the composition given by the liquidus line, since diffusion is relatively rapid in liquid. At T3 the average solid solution will be of composition α’3 instead of α3.  Under equilibrium cooling, solidification should be complete at T4 ; however, since the average composition of the solid solution α’4 has not reached the composition of the alloy, some liquid must still remain. Applying lever rule at T4 gives α’4 = 75% and L4 = 25%. 44  Therefore, solidification will continue until T5 is reached. At this temperature the composition of the solid solution α’5 coincides with the alloy composition, and solidification is complete. The last liquid to solidify, L5, is richer in B than the last liquid to solidify under equilibrium conditions.  The more rapidly the alloy is cooled the greater will be the composition range in the solidified alloy. Since the rate of chemical attack varies with composition, proper etching will reveal the dendritic structure microscopically (see below figure). The final solid consists of a “cored” structure with a higher-melting central portion surrounded by the lower-melting, last-to-solidify shell. The above condition is referred to as coring or dendritic segregation.  To summarize, nonequilibrium cooling results in an increased temperature range over which liquid and solid are present; Since diffusion has not kept pace with crystal growth, there will be a difference in chemical composition from the center to the outside of the grains. The faster the rate of cooling, the greater will be the above effects. Eutectic Phase Diagram Very few systems exhibit an isomorphous phase diagram (usually the solid solubility of one component in another is limited). Often the solid solubility is severely limited – through the solid solubility is never zero (due to entropic reasons). In a Simple eutectic system (binary), there is one composition at which the liquid freezes at a single temperature. This is in some sense similar to a pure solid which freezes at a single temperature (unlike a pure substance the freezing produces a two solid phases both of which contain both the components). The term Eutectic means easy melting → The alloy of eutectic composition freezes at a lower temperature than the melting point s of the constituent components. This has important implifications → e.g. the Pb -Sn eutectic alloy melts at 183 ºC, which is lower than the melting points of both Pb (327ºC) and Sn (232ºC)→ Can be used for soldering purposes (as we want to input least amount of heat to solder two materials). In the next page we consider the Pb-Sn eutectic phase diagram. 45 Microstructural Characteristics of Eutectic System  To reiterate an important point: Phase diagram do not contain microstructural information (i.e. they cannot tell you what the microstructures produced by cooling is. Often microstructural information is overlaid on phase diagram for convenience. Hence, strictly cooling is not in the domain of phase diagram – but we can overlay such information keeping in view the assumptions involved. 46 Application of Lever rule in Eutectic System Peritectic Phase Diagram 47  Like the eutectic system, the Peritectic reaction is found in systems with complete liquid solubility but limited solid solubility. In the Peritectic reaction the liquid (L) reacts with one solid (α) to produce another solid (β). L+α → β Since the solid β forms at the interface between the L and the α, further reaction is dependent on solid state diffusion. Needless to say this becomes the rate limiting step and hence it is difficult to ‘equilibrate’ peritectic reactions (as compared to say eutectic reactions). In some Peritectic reactions (e.g. the Pt-Ag system – previous page). The (pure) β phase is not stable below the Peritectic temperature (TP = 1186 ºC for Pt- Ag system) and splits into a mixture of (α+β) just below TP. Monotectic Phase Diagram In all the types discussed previously, it was assumed that there was complete solubility in the liquid state. It is quite possible, however, that over a certain composition range two liquid solutions are formed that are not soluble in each other. Another term for solubility is miscibility. Substances that are not soluble in each other, such as oil and water, are said to be immiscible. Substances that are partly soluble in each other are said to show a miscibility gap, and this is related to Monotectic Systems. When one liquid forms another liquid, plus a solid, on cooling, it is known as a Monotectic Reaction. It should be apparent that the Monotectic reaction resembles the eutectic reaction, the only difference being that one of the products is a liquid phase instead of a solid phase. 48  An example of an alloy system showing a Monotectic reaction is that between copper and lead given in next page. Notice that in this case the L1 + L2 is closed. Also, although the terminal solids are indicated as α and β, the solubility is actually so small that they are practically the pure metals, copper and lead. The Eutectoid Reaction  This is a common reaction in the solid state. It is very similar to the eutectic reaction but does not involve the liquid. In this case, a solid phase transforms on cooling into two new solid phases. The general equation may be written as..!  The resultant Eutectoid mixture is extremely fine, just like the eutectic mixture. Under the microscope both mixtures generally appear the same, and it is not possible to determine microscopically whether the mixture resulted from a eutectic reaction or eutectoid reaction.  An equilibrium diagram of Cu-Zn, illustrating the eutectoid reaction is shown in figure.  In copper (Cu) – Zinc (Zn) system contains two terminal solid solutions i.e. these are extreme ends of phase diagram α and η, with four intermediate phases called β, γ, δ and ε. The β’ phase is termed an ordered solid solution, one in which the copper and zinc atoms are situated in a specific and ordered arrangement within each unit cell. 49  In the diagram, some phase boundary lines near the bottom are dashed to indicate that there positions have not been exactly determined. The reason for this is that at low temperatures, diffusion rates are very slow and inordinately long times are required for the attainment of equilibrium. Again only single- and two- phase regions are found on the diagram, and the same and we can utilize the lever rule for computing phase compositions and relative amounts. The commercial material brasses are copper-rich copper-zinc alloys: for example, cartridge brass has a composition of 70 wt% Cu-30 wt% Zn and a microstructure consisting of a single α phase. The Peritectoid Reaction This is a fairly common reaction in the solid state and appears in many alloy systems. The peritectoid reaction may be written as The new solid phase is usually an intermediate alloy, but it may also be a solid solution.The peritectoid reaction has the same relationship to the peritectic reaction as the eutectoid has to the eutectic. Essentially, it is the replacement of a liquid by a solid. 50  The peritectoid reaction occurs entirely in the solid state and usually at lower temperatures than the peritectic reaction, the diffusion rate will be slower and there is less likelihood that equilibrium structures will be reached. Consider Silver (Ag) – Aluminium (Al) phase diagram (in next page) containing a peritectoid reaction. If a 7% Al alloy is rapidly cooled from the two phase area just above the peritectoid temperature the two phases will be retained, and the microstructure will show a matrix of γ with just a few particles of α. When we cool at below the peritectoid temperature by holding we get single phase μ. Monotectoid Reaction : Al-Zn Phase Diagram 51 Syntectic Reaction : Ga – I Phase Diagram Summary of Invariant reactions 52 Allotropic Transformations As we discussed earlier that several metals may exist in more than one type of crystal structure depending upon temperature , Iron, Tin, Manganese and Cobalt are examples of metals which exhibit this property , known as Allotropy. On an equilibrium diagram, this allotropic change is indicated by a point or points on the vertical line which represents the pure metal. This is illustrated in below figure. In this diagram, the gamma solid solution field is ‘looped’. The pure metal Fe and alloys rich in Fe undergo two transformations. Order-disorder Transformations Ordinarily in the formation of substitutional type of solid solution the solute atoms do not occupy any specific position but are distributed at random in the lattice structure of the solvent. The alloy is said to be in a ‘disordered’ condition. 53  Some of these random solid solutions, if cooled slowly, undergo a rearrangement of the atoms where the solute atoms move into definite positions in the lattice. This structure is known as an ordered solid solution or superlattice. Ordering is most common in metals that are completely soluble in the solid state, and usually the maximum amount of ordering occurs at a simple atomic ratio of the two elements. For this reason, the ordered phase is sometimes given a chemical formula, such as AuCu and AuCu3 in the gold-copper alloy system. On the equilibrium diagram, the ordered solutions are frequently designated as α , β , etc. or α , α , etc., and the area in which they are found is usually bounded by a dot-dash line. When the ordered phase has the same lattice structure as the disordered phase, the effect of ordering on mechanical properties is negligible. Hardening associated with the ordering process is most pronounced in those systems where the shape of the unitcell is changed by ordering. Regardless of the structure formed as a result of ordering, an important property change produced, even in the absence of hardening, is a significant reduction in electrical resistance. Notice the sharp decrease in electrical resistivity at the compositions which correspond to the ordered phases AuCu and AuCu3. Allotropic Transformations in Iron Iron is an allotropic metal, which means that it can exist in more than one type of lattice structure depending upon temperature. A cooling curve for pure iron is shown below: 54 Iron – Cementite Phase Diagram The Fe-C (or more precisely the Fe-Fe3C) diagram is an important one. Cementite is a metastable phase and ‘strictly speaking’ should not be included in a phase diagram. But the decomposition rate of cementite is small and hence can be thought of as ‘stable enough’ to be included in a phase diagram. Hence, we typically consider the Fe-Fe3C part of the Fe-C phase diagram. A portion of the Fe-C diagram – the part from pure Fe to 6.67 wt.% carbon (corresponding to cementite, Fe3C) – is technologically very relevant. Cementite is not a equilibrium phase and would tend to decompose into Fe and graphite. This reaction is sluggish and for practical purpose (at the microstructural level) cementite can be considered to be part of the phase diagram. Cementite forms as it nucleates readily as compared to graphite. Compositions upto 2.1%C are called steels and beyond 2.1% are called cast irons. In reality the calssification should be based on ‘castability’ and not just on carbon content. Heat treatments can be done to alter the properties of the steel by modifying the microstructure → we will learn about this in coming chapters. 55 Figure: Iron – Cementite Phase Diagram Carbon Solubility in Iron Solubility of carbon in Fe = f (structure, temperature) Where is carbon located in iron lattice? 56 Characteristics of phases appeared in Fe-Fe3C phase diagram Ferrite (α) It is an interstitial solid solution of a small amount of carbon dissolved in α iron. The maximum solubility is 0.025%C at 723ºC and it dissolves only 0.008%C at room temperature. It is the softest structure that appears on the diagram The crystal structure of ferrite (α) is B.C.C Tensile strength – 40,000 psi or 275 Mpa Elongation – 40% in 2 in. Hardness - < 0 HRC or < 90 HRB Cementite (Fe3C) Cementite or iron carbide, chemical formula Fe3C, contains 6.67%C by weight and it is a metastable phase. It is typically hard and brittle interstitial compound of low tensile strength (approx. 5000 psi) but high compressive strength. It is the hardest structure that appears on the diagram. Its crystal structure is orthorhombic 57 Pearlite (α + Fe3C)  Pearlite is the eutectoid mixture containing 0.80 %C and is formed at 723ºC on very slow cooling.  It is very fine platelike or lamellar mixture of ferrite and cementite. The fine fingerprint mixture called pearlite is shown in below figure.  Tensile strength – 120,000 psi or 825 Mpa  Elongation – 20 percent in 2 in.  Hardness – HRC 20, HRB 95-100, or BHN 250-300 Austenite (γ)  It is an interstitial solid solution of a small amount of carbon dissolved in γ iron. The maximum solubility is 2.1%C at 1147ºC.  The crystal structure of Austenite (γ) is F.C.C  Tensile strength – 150,000 psi or 1035 Mpa  Elongation – 10% in 2 in.  Hardness - 40 HRC and Toughness is high. Ledeburite (γ+ Fe3C) Ledeburite is the eutectic mixture of austenite and cementite. It contains 4.3%C and is formed at 1147ºC Structure of ledeburite contains small islands of austenite are dispersed in the carbide phase. Not stable at room temperature Ferrite (δ) Interstitial solid solution of carbon in iron of body centered cubic crystal structure. (δ iron ) of higher lattice parameter (2.89Å) having solubility limit of 0.09 wt% at 1495°C with respect to austenite. The stability of the phase ranges between 1394- 1539°C. 58  This is not stable at room temperature in plain carbon steel. However it can be present at room temperature in alloy steel especially duplex stainless steel. Microstructures involved in eutectoid mixture \ Eutectoid reaction Phase changes that occur upon passing from the γ region into the α+ Fe3C phase field. Consider, for example, an alloy of eutectoid composition (0.8%C) as it is cooled from a temperature within the γ phase region, say 800ºC – that is, beginning at point ‘a’ in figure and moving down vertical xx’. Initially the alloy is composed entirely of the austenite phase having composition 0.8 wt.% C and then transformed to α+ Fe3C [pearlite] The microstructure for this eutectoid steel that is slowly cooled through eutectoid temperature consists of alternating layers or lamellae of the two phases α and Fe3C The pearlite exists as grains, often termed “colonies”; within each colony the layers are oriented in essentially the same direction, which varies from one colony to other. The thick light layers are the ferrite phase, and the cementite phase appears as thin lamellae most of which appear dark. 59 Hypo eutectoid region  Hypo eutectoid region – 0.008 to 0.8 %C  Consider vertical line yy’ in figure, at about 875ºC, point c, the microstructure will consist entirely of grains of the γ phase.  In cooling to point d, about 775ºC, which is within the α+γ phase region, both these phases will coexist as in the schematic microstructure Most of the small α particles will form along the original γ grain boundaries.  Cooling from point d to e, just above the eutectoid but still in the α+γ region, will produce an increased fraction of the α phase and a microstructure similar to that also shown: the α particles will have grown larger.  Just below the eutectoid temperature, at point f, all the γ phase that was present at temperature e will transform pearlite. Virtually there is no change in α phase that existed at point e in crossing the eutectoid temperature – it will normally be present as a continuous matrix phase surrounding the isolated pearlite colonies.  Thus the ferrite phase will be present both in the pearlite and also as the phase that formed while cooling through the α+γ phase region. The ferrite that is present in the pearlite is called eutectoid ferrite, whereas the other, is termed proeutectoid (meaning pre- or before eutectoid) ferrite. Hyper eutectoid region Hyper eutectoid region – 0.8 to 2.1 %C Consider an alloy of composition C1 in figure that, upon cooling, moves down the line zz’. At point g only the γ phase will be present and the microstructure having only gamma grains. Upon cooling into the γ+ Fe3C phase field – say to point h – the cementite phase will began to form along the initial γ grain boundaries, similar to the α phase in point d. this 60  cementite is called proeutectoid cementite that which forms before the eutectoid reaction. As the temperature is lowered through the eutectoid to point I, all remaining austenite of eutectoid composition is converted into pearlite; thus the resulting microstructure consists of pearlite and proeutectoid cementite as microconstituents. Application of Lever rule in Fe-Fe3C phase diagram 61 Critical temperature lines In general, A0 – Subcritical temperature, A1 - lower critical temperature, A3 - upper critical temperature, A4 – Eutectic temperature, A5 – Peritectic temperature and Acm - γ/γ+cementite phase field boundary. While heating we denoted as Ac1, Ac2, Ac3 etc., ‘c’ stands for chauffage (French word), which means heating and while cooling we denoted as Ar1, Ar2, Ar3 etc., ‘r’ stands for refroidissement, (French word) which means cooling. Martensitic Transformations 62  Under slow cooling rates, the carbon atoms are able to diffuse out of the austenite structure and it leads to gamma to alpha transformation. This process involves nucleation and growth and it is time dependent. With a still further increase in cooling rate, insufficient time is allowed for the carbon to diffuse out of solution, and although some movement of the iron atoms takes place, the structure cannot become B.C.C. while the carbon is trapped in solution. The resultant structure is called Martensite, is a supersaturated solid solution of carbon trapped in a body-centered tetragonal structure and it is a metastable phase. The highly distorted lattice structure is the prime reason for the high hardness of martensite. After drastic cooling, martensite appears microscopically as a white needlelike or acicular structure or lenticular, sometimes described as pile of straw. Shape of the Martensite formed →Lenticular (or thin parallel plates) Associated with shape change (shear) This condition requires: o Bain distortion → Expansion or contraction of the lattice along certain crystallographic directions leading to homogenous pure dilation o Secondary Shear Distortion →Slip or twinning o Rigid Body rotation Martensitic transformation can be understood by first considering an alternate unit cell for the Austenite phase as shown in the figure below. If there is no carbon in the Austenite (as in the schematic below), then the Martensitic transformation can be understood as a ~20% contraction along the c-axis and a ~12% expansion of the a-axis → accompanied by no volume change and the resultant structure has a BCC lattice (the usual BCC-Fe) → c/a ratio of 1.0. 63  In the presence of Carbon in the octahedral voids of CCP (FCC) γ-Fe (as in the schematic below) → the contraction along the c-axis is impeded by the carbon atoms. (Note that only a fraction of the octahedral voids are filled with carbon as the percentage of C in Fe is small). However the a1 and a2 axis can expand freely. This leads to a product with c/a ratio (c’/a’) >1 In this case there is an overall increase in volume of ~4.3% (depends on the carbon content) → the Bain distortion. The Martensitic transformation occurs without composition change The transformation occurs by shear without need for diffusion and is called diffusion less transformation The atomic movements (shearing) required are only a fraction of the inter atomic 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 64  Steel is reheated to increase its ductility → this process is called TEMPERING The martensite transformation, for many years, was believed to be unique for steel. However, in recent years, this martensite type of transformation has been found in a number of other alloy systems, such as iron-nickel, copper-zinc, and copper-aluminum. The basic purpose of hardening is to produce a fully martensitic structure, and the minimum cooling rate ( per second) that will avoid the formation of any of the softer products of transformation is known as the critical cooling rate. The critical cooling rate, determined by chemical composition and austenitic grain size, is an important property of a steel since it indicates how fast a steel must be cooled in order to form only martensite Time-Temperature-Transformation (TTT) Diagrams Davenport and Bain were the first to develop the TTT diagram of eutectoid steel. They determined pearlite and bainite portions whereas Cohen later modified and included MS and MF temperatures for martensite. There are number of methods used to determine TTT diagrams. The most popular method is salt bath techniques combined with metallography and hardness measurement with addition of this we have other techniques like dilatometry, electrical resistivity method, magnetic permeability, in situ diffraction techniques (X-ray, neutron), acoustic emission, thermal measurement techniques, density measurement techniques and thermodynamic predictions. TTT diagrams, also called as Isothermal (temperature constant) Transformation diagrams. TTT diagrams give the kinetics of isothermal transformations. For every composition of steel we should draw a different TTT diagram. For the determination of isothermal transformation (or) TTT diagrams, we consider molten salt bath technique combined with metallography and hardness measurements. In molten salt bath technique two salt baths and one water bath are used. Salt bath I is maintained at austenising temperature (780˚C for eutectoid steel). Salt bath II is maintained at specified temperature at which transformation is to be determined (below Ae1), typically 700-250°C for eutectoid steel. Bath III which is a cold water bath is maintained at room temperature. In bath I number of samples are austenite at A1+20-40°C for eutectoid, A3+20-40°C for hypo-eutectoid steel and ACm+20-40°C for hyper-eutectoid steels for about an hour. Then samples are removed from bath I and put in bath II and each one is kept for different specified period of time say t1, t2, t3, t4,…..........,tn etc. After specified times, the samples are removed and quenched in cold water. The microstructure of each sample is studied using metallographic techniques. The type, as well as quantity of phases, is determined on each sample. 65  As pointed out before one of the important utilities of the TTT diagrams comes from the overlay of micro-constituents (microstructures) on the diagram.  Depending on the T, the (γ+ Fe3C) phase field is labeled with micro-constituents like Pearlite, Bainite. 66  The time taken to 1% transformation to, say pearlite or bainite is considered as transformation start time and for 99% transformation represents transformation finish.  We had seen that TTT diagrams are drawn by instantaneous quench to a temperature followed by isothermal hold.  Suppose we quench below (~225°C, below the temperature marked Ms), then Austenite transforms via a diffusionless transformation (involving shear) to a (hard) phase known as Martensite. Below a temperature marked Mf this transformation to Martensite is complete. Once γ is exhausted it cannot transform to (γ + Fe3C).  Hence, we have a new phase field for Martensite. The fraction of Martensite formed is not a function of the time of hold, but the temperature to which we quench (between Ms and Mf).  Strictly speaking cooling curves (including finite quenching rates) should not be overlaid on TTT diagrams (remember that TTT diagrams are drawn for isothermal holds!). TTT diagram for Hypo eutectoid steel  In hypo- (and hyper-) eutectoid steels (say composition C1) there is one more branch to the ‘C’ curve-NP (next slide: marked in red). 67  The part of the curve lying between T1 and TE (marked in fig : next slide) is clear, because in this range of temperatures we expect only pro-eutectoid α to form and the final microstructure will consist of α and γ. (E.g. if we cool to Tx and hold).  The part of the curve below TE is a bit of a ‘mystery’ (since we are instantaneously cooling to below TE, we should get a mix of α+ Fe3C what is the meaning of a ‘pro’-eutectoid phase in a TTT diagram? (remember ‘pro-’ implies ‘pre-’)  Suppose we quench instantaneously an hypo-eutectoid composition C1 to Tx we should expect the formation of α+Fe3C (and not pro-eutectoid α first).  The reason we see the formation of pro-eutectoid α first is that the undercooling w.r.t to Acm is more than the undercooling w.r.t to A1. Hence, there is a higher propensity for the formation of pro-eutectoid α. TTT diagram for Hyper eutectoid steel  Similar to the hypo-eutectoid case, hyper-eutectoid compositions C2 have a γ+Fe3C branch.  For a temperature between T2 and TE (say Tm (not melting point- just a label)) we land up with γ+Fe3C.  For a temperature below TE (but above the nose of the ‘C’ curve) (say Tn), first we have the formation of pro-eutectoid Fe3C followed by the formation of eutectoid γ+Fe3 C. 68 Transformation to Pearlite The transformation product above the nose region is pearlite. The pearlite microstructure is the characteristic lamellar structure of alternate layers of ferrite and cementite. As the transformation temperature decreases, the characteristic lamellar structure is maintained, but the spacing between the ferrite and carbide layers becomes increasingly smaller until the separate layers cannot be resolved with the light microscope. As the temperature of transformation and the fineness of the pearlite decreases, it is apparent that the hardness will increase. 69  Nucleation and growth Heterogeneous nucleation at grain boundaries Interlamellar spacing is a function of the temperature of transformation Lower temperature → finer spacing → higher hardness Transformation to Bainite 70  In between the nose region of approximately 510˚C and the M s temperature, a new, dark-etching aggregate of ferrite and cementite appears. This structure, named after E.C.Bain, is called bainite. At upper temperatures of the transformation range, it resembles pearlite and is known as upper or feathery bainite. At low temperatures it appears as a black needlelike structure resembling martensite and is known as lower or acicular banite.  Pearlite is nucleated by a carbide crystal, bainite is nucleated by a ferrite crystal, and this results in a different growth pattern.  Acicular, accompanied by surface distortions  ** Lower temperature → carbide could be ε 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 Continuous Cooling Transformation diagrams  The TTT diagrams are also called Isothermal Transformation Diagrams, because the transformation times are representative of isothermal hold treatment (following a instantaneous quench). 71  In practical situations we follow heat treatments (T-t procedures/cycles) in which (typically) there are steps involving cooling of the sample. The cooling rate may or may not be constant. The rate of cooling may be slow (as in a furnace which has been switch off) or rapid (like quenching in water).  Hence, in terms of practical utility TTT curves ha