MSE 260 PHASE TRANSFORMATIONS Dr. Emmanuel Gikunoo Department of - PowerPoint PPT Presentation

THERMODYNAMICS OF PHASE CHANGES From definition,   = G  , where g  is the molar free energy of the  phase Similarly ,   = G  At equilibrium and from the expression, dG = – sdT + vdP dG  = – s  dT + v  dP = dG  = – s  dT + v  dP Or, (v  – v  )dP = (s  – s  )dT 23

THERMODYNAMICS OF PHASE CHANGES For isothermal transformations and at equilibrium,  g =  h – T  s = 0 where  h mostly represents the latent heat of transformation Hence, This is known as the Clausius–Clayperon equation The equation shows the relationship between pressure and temperature at which phases  and  exist in equilibrium. It also shows the enthalpy and volume changes that accompany such changes 24

HEAT EFFECTS ACCOMPANYING PHASE CHANGES OF PURE SUBSTANCES Clausius–Clayperon equation But Hence approximate relation (Clausius – Clapeyron equation) 𝑤 𝑤 𝑤 2 where the 25

Gibb’s Phase Rule  Gibb’s phase rule describes the thermodynamic state of a material.  It also states the degree of freedom available to describe a particular system with various phases and substances F = C – P + v F = number of degrees of freedom The number of variables to define a system in a phase diagram P = number of phases Phases are mechanically separable constituents C = minimum number of components chemical constituents that must be specified in order to define all phases 26

Gibb’s Phase Rule F = C – P + v F = number of degrees of freedom The number of variables to define a system in a phase diagram P = number of phases Phases are mechanically separable constituents C = minimum number of components chemical constituents that must be specified in order to define all phases v = intensive properties or materials variables P/T and pH/Eh diagrams = 2 27

Gibb’s Phase Rule  Gibbs phase rule works best in (constructing) a phase diagram. And those are usually 2-dimensional - with pressure along one axis and temperature the other. So the "2" simply reflects that 2 dimensionality.  At 2 degrees of freedom, there are no constraints and the system can change either pressure or temperature and be stable without a phase transition.  If you have 1 degree of freedom, then you likely to have a constraint  These are not really constants, but if the degrees of freedom is 0, then they are ... "fixed‘' – or better yet "constrained". 28

Merits of the Phase Rule 1. It is applicable to both physical and chemical equilibria. 2. It requires no information regarding molecular/microstructure, since it is applicable to macroscopic systems. 3. It is a convenient method of classifying equilibrium states in terms of phases, components and degrees of freedom. 4. It helps us to predict the behaviour of a system, under different sets of variables. 5. It indicates that different systems with same degree of freedom behave similarly. 6. It helps in deciding whether under a given set of conditions: a) various substances would exist together in equilibrium, or b) some of the substances present would be interconverted, or c) some of the substances present would be eliminated. 29

Limitations of Phase Rule 1. It can be only be applied to systems in equilibrium. Consequently, it is of little value in case of very slow equilibrium state attaining system. 2. It applies only to a single equilibrium system; and provide no information regarding any other possible equilibria in the system. 3. Phases existing in the equilibrium state must be carefully stated, since it considers only the number of phases, rather than their amounts. Thus even if a trace of phase is present, it accounts towards the total number of phases. 4. All phases of the system must be present simultaneously under the identical conditions of temperature and pressure. 5. Solid and liquid phases must not be in finely-divided state; otherwise deviations will occur. 30

Phase Diagrams  A phase is a state of matter with the following characteristics: It has the same structure or atomic arrangement throughout  It has roughly the same composition and properties throughout  There exists a definite interface between it and its surroundings or  adjoining phases  A phase diagram is a graphical representation of the phases that are present in a material at various temperatures, pressures and compositions It usually describes the equilibrium conditions  Sometimes non-equilibrium conditions are also shown when well  known. It indicates the melting/solidification temperatures of the constituents  It indicates the compositions of alloys where solidification begins and  the temperature range over which it occurs  Phase transformation – is an alteration in the number and/or character of the phases in the system 31

Phase Diagrams Phase Diagrams: The diagram representing conditions of temperature, pressure and composition at which one or more phases exit together. Phase Diagram of Water System: Fusion Curve Critical 2 phases Point P c Solid Liquid (1 phase) Pressure (1 phase) Vapor Pressure Curve (2 phases) Vapor (1 phase) Triple Point (3 phases) Sublimation Curve (2 phases) 32 T c Temperature

Phase Diagrams Phase Diagram of Water System: 33

Phase Diagrams  Some important features of Water System: Possible phases : Ice (s), Water(l), Vapour (g)  Curves: three stable curves throughout  OA ( Vapour pressure curve, Water  Vapour) o OB ( Sublimation Curve, Ice  Vapour) o OC ( Melting point curve, Ice  Water) o One metastable curve OA'  (Vapour pressure curve of super cooled water) o Areas : Three areas representing ice, water and vapour.  Triple point (O): Where all the three phases are in  equilibrium (0.0098 o C and 4.58 mm pressure).  The melting point curve OC has a negative slope, showing that the melting point of ice decreases with increase of pressure 34

Phase Diagrams Phase Diagram of Sulphur System: 35

Phase Diagrams  Some important features of Sulphur System: Possible phases : Rhombic sulphur (S R ), monoclinic sulphur  (S R ), sulphur vapour (S V ) and sulphur liquid (S L ). Maximum phases: If P = 4, then F = C – P + 2 = 1 – 4 + 2  = –1 Which is meaningless. Hence all the four phases cannot coexist. Areas : Four areas containing one phase each  Curves: there are six stable curves  Sublimation curve of S R o Sublimation curve of S M o Vapour pressure curve of S L o T ransition curve of S R o Melting curve of S M o 36 Melting curve of S R o

Phase Diagrams  Some important features of Sulphur System: Metastable curves : There are four metastable curves  Sublimation curve of S R o Sublimation curve of S M o o Vapour pressure curve of S L o Melting curve of S R Triple point (O): There are three stable triple points S R -S M -S V ,  S M -S L -S V , S R -S M -S L and one metastable triple point S R -S L -S V . 37

Phase Diagrams The system SiO 2 T wo variables: P and T One component : SiO 2 7 different phases Point A: F = C – P + 2 F = 1 – 1 + 2 A F = 2 Divariant area = T wo variables to define a position in the coesite stability field 38

Phase Diagrams The system SiO 2 T wo variables: P and T One component : SiO 2 7 different phases Point B: F = C – P + 2 F = 1 – 2 + 2 F = 1 B Univariant area = One variable to define a position on the coesite – α-quartz phase boundary 39

Phase Diagrams The system SiO 2 T wo variables: P and T One component : SiO 2 7 different phases Point C: F = C – P + 2 F = 1 – 3 + 2 F = 0 C Invariant area = T riple point do not need any variable to define equilibrium between coesite – α- and β-quartz 40

General Types of Alloys  There are two general types of alloys having phase diagrams.  Substitutional alloys  Interstitial alloys  Subtitutional alloys have elements, which are incorporated into regular lattice positions within the unit cell  An example is Sn and Zn alloying additions to Cu to form bronze and brass, respectively  Hume Rothery rules of solid solubility  Interstitial alloys have elements, which are incorporated into the interstitial sites of the unit cell  An example is carbon in iron to form steel 41

Two Components Phase Diagrams  Application of Phase Rule to two component systems: As C = 2, minimum P = 1 and hence minimum F = C – P + 2 = 3. Thus the three variables (pressure, temperature and composition) should be plotted. But for convenience, two dimension diagrams are plotted by keeping the third variable constant. Hence we have P – T , C – P , or T – C diagrams. Generally pressure is kept constant at atmospheric pressure and we have T – C diagrams.  Reduced phase rule: If pressure is kept constant then the degree of freedom is reduced by one and hence the phase rule equation becomes C – P + 1 42

Two Components Phase Diagrams T ypes of T wo Component Systems:  T ype 1: T wo metals completely soluble in both liquid and solid states – Isomorphous T wo metals completely o soluble in the solid state, type of solid phase formed will be the substitution solid solution. The diagram shows the series o of cooling curves for different alloys in a completely soluble system. The dotted lines form the phase diagram The diagram plots o temperature vs. composition. 43

Two Components Phase Diagrams T ypes of T wo Component Systems:  T ype 2: T wo metals completely soluble in the liquid state and completely insoluble in the solid state One liquid solution. o Solids A and B mix to o form a two phase solid The point at which the o liquidus lines intersect the minimum point E, is known as the eutectic point. TE is called the eutectic o temperature. 44

Two Components Phase Diagrams T ypes of T wo Component Systems:  T ype 3: T wo metals completely soluble in the liquid state but only partly soluble in the solid state One liquid solution. o Solids α and β mix to o form a two phase solid 45

Working with Phase Diagrams Overall composition  Solidus  Liquidus  Limits of solid solubility  Chemical composition of phases at any temperature  Amount of phases at any temperature  Invariant reactions  Development of microstructure  46

Working with Phase Diagrams Cooling curves  Differential scanning calorimetry  Thermomechanical analysis  Differential thermal analysis  Metallography/petrography  Energy dispersive X-ray spectroscopy  Electron microprobe analyzer  X-ray diffraction  Transmission electron microscope  47

Phase Diagrams - Two Component Cooling Curves  The liquidus temperature is the temperature above which a material is completely liquid  The solidus temperature is the temperature below which the alloy is 100 % solid  The freezing range of the alloy is the temperature difference between the liquidus and solidus where the two phases exists, i.e., the liquid and solid Cooling curve for an isomorphous alloy during solidification. The changes in slope of the cooling curve indicate the liquidus and solidus 48 temperatures.

Cooling Curves  Series of cooling curves at different metal compositions are first constructed  Points of change of slope of cooling curves (thermal arrests) are noted and used in the construction of phase diagram  Pure metals solidifies at a constant temperature which is known as the melting temperature  Binary alloys solidify over a range of temperatures 49

Isomorphous Phase Diagrams  When only two elements or two compounds are present in a material a “binary phase diagram” can be constructed.  In isomorphous binary phase diagrams, only one solid phase forms as the two components in the system display complete solid solubility.  Examples include the Cu-Ni and NiO-MgO systems. Note that the concentrations can be expressed in wt.% or mole %. 50

Isomorphous Systems Systems With Complete Solid Solution Plagioclase (Ab-An, NaAlSiO 8 - CaAl 2 Si 2 O 8 ) Liquidus = a curve or a surface along which compositions of a melt are in equilibrium with a crystalline phase. Solidus = a curve or a surface along which compositions of a crystalline phase are in equilibrium with a melt. 51

Amount of Phases in Binary Alloys  The Lever Rule is used to calculate the weight % of the phase in any two- phase region of the phase diagram (and only the two phase region!) C o  In general:  Example, for the liquid – solid ( C L – C S ) region, the weight fractions of  When an alloy is present in a � � two phase region, a tie line at � the temperature of interest fixes � � the composition of the two � � phases. � � �  This is a consequence of the where C L = the liquid composition, Gibbs phase rule, which C S = the solid composition, and provides for only one degree of C O = the bulk composition 52 freedom.

Determination of Phase(s) Present • Rule 1: If we know T and C o , then we must know: how many phases and which phases are present.  T(°C) 1600 • Example: L (liquid) 1500 Melting points: liquidus B(1250,35) Cu = 1085 ° C s u 1400 d i l o Ni = 1453 °C s L +   1300 (FCC solid 1200 A (1100  C, 60 wt.% Ni): solution) 1 phase: α 1100 A(1100,60) B (1250  C, 35 wt.% Ni): 2 phases: L + α 1000 wt% Ni 0 20 40 60 80 100 Cu-Ni system 53

Composition of Phase(s) • Rule 2: If we know T and C o , then we must know: the composition of each phase  • Example: T(°C) At T A = 1320  C A TA s tie line u d O nly liquid (L) present i u q i L (liquid) l 1300 L +  C L = C 0 (35 wt.% Ni) solidus B At T D = 1190  C TB  Only solid ( α ) present L +  (solid) C α = C 0 (35 wt.% Ni) 1200 D TD At T B = 1250  C 32 35 43 20 30 40 50 Both α and L present CL Co C  wt% Ni C L = C liquidus (32 wt.% Ni) Cu-Ni system C α = C solidus (43 wt.% Ni) 54

Weight Fraction of Phase(s) • Rule 3: If we know T and C o , then we must know: the amount of each phase (given in wt.%)  • Example: C o = 35 wt.% Ni At T A = O nly liquid (L) W L = 100 wt.%, W α = 0 At T D = Only solid ( α ) W L = 0, W α = 100 wt.% At T B = Both α and L � � � � � �� ��� W L = � � � � � �� ��� � � � � � �� ��� W α = Cu-Ni system � � � � � �� ��� 55

Solidification of a Solid-Solution Alloy  Change in structure and composition of a Cu – 40 % Ni alloy during equilibrium solidification  Liquid contains 40 % Ni and the first solid contains Cu – 52 % Ni.  At 1250  C, solidification has advanced and the phase diagram of the liquid contains 32 % Ni and the solid 45 % Ni, which continues until just below the solidus.  Solid contains 40 % Ni, which is achieved through 56 diffusion.

Solidification of a Solid-Solution Alloy  When cooling is too fast for atoms to diffuse and produce equilibrium conditions, nonequilibrium concentrations are produced.  The first solid formed contains 52 % Ni and the last solid only 25 % Ni with the last liquid containing only 17 % Ni. The average composition of Ni is 40 % but it is not uniform. 57

Cored vs Equilimbrium Phases 58

Microsegregation and Homogenization  The nonuniform composition produced by nonequilibrium solidification is known as segregation  Microsegregation, also known as interdendritic segregation and coring, occurs over short distances on the micron length scale  Microsegregation can cause hot shortness which is the melting of the material below the melting point of the equilibrium solidus  Homogenization, which involves heating the material just below the non-equilibrium solidus and holding it there for a few hours, reduces the microsegregation by enabling diffusion to bring the composition back to equilibrium  Macrosegregation can also exist where there exist a large composition difference between the surface and the center of a casting, which cannot be affected by diffusion as the distance is too large  Hot working breaks down the cast macrostructure enabling the 59 composition to be evened out

Rapidly Solidified Powders  Many complex metal alloys are made by rapidly solidifying a spray of fine droplets of material, usually consisting of complex compositions, in a quenching gas such as argon, nitrogen or water.  Examples are nickel- and cobalt-based super alloys and some stainless steels.  This process minimizes microsegregation, macrosegregation and porosity since the process happens so rapidly that there is no time for segregation or diffusion.  The fine particles are then processed into shapes using sintering, hot pressing and hot isostatic pressing (HIP). 60

Mechanical Properties: Cu – Ni System 61

Binary Phase Diagrams – Limited Solubility Not all metals are completely soluble in each other.  Distinctions can be made between two types solid solutions with limited solubility – (i) Eutectic and (ii) Peritectic. When the melting points of two metals are comparable, a  eutectic system forms while a peritectic results when melting points are significantly different. A eutectic reaction is defined as the one which generates two  solids from the liquid at a given temperature and composition, L → α + β Peritectic is Liquid + Solid 1 → Solid 2 ( L + α → β )  In both cases three phases (two solids and a liquid) coexist and  the degrees of freedom F = 2 – 3 + 1 = 0. This is known as invariant (F = 0) reaction or transformation. 62

Eutectic Phase Diagrams • Many alloy systems are based on only two elements. • A good example is the lead – tin system, which is used for soldering but because of the toxicity of Pb, it is now being replaced with other Sn alloys. Solid Solution Alloys • A single phase solid solution forms during solidification. • Examples include Pb – 2 wt.% Sn. • These alloys strengthen by solid-solution strengthening, by strain hardening and by controlling the solidification process to refine the grain structure. 63

Eutectic Phase Diagrams Partially Soluble in the Solid Phase In the eutectic system  between two metals A and B, two solid solutions, one rich in A ( α ) and another rich in B ( β ) form. Eutectic isoterm In addition to  liquidus and solidus lines there are two more lines on A and B rich ends which define the solubility limits B in A and A in B respectively. These 64 are called solvus lines.

Eutectic Phase Diagrams Completely Insoluble in the Solid Phase In this eutectic  system, two compounds are completely soluble in each other in the liquid phase but insoluble in each other in the solid phase. i.e. they exists as independent crystals in the solid phase. There are the liquidus  and solidus lines but no solvus lines. 65

Eutectic Phase Diagrams Three phases ( L + α + β ) coexist at point E. This point is called  eutectic point or composition. Left of E is called hypoeutectic whereas right of E is called hypereutectic. A eutectic composition solidifies as a eutectic mixture of α and β  phases. The microstructure at room temperature (RT) may consist of alternate layers or lamellae of α and β . In hypoeutectic alloys the α phase solidifies first and the  microstructure at RT consists of this α phase (called proeutectic α ) and the eutectic ( α + β ) mixture. Similarly hypereutectic alloys consist of proeutectic β and the eutectic mixture. The melting point at the eutectic point is minimum. Other  eutectic systems are Ag-Cu, Al-Si, Al-Cu. 66

Eutectic Cooling Curves While cooling a hypoeutectic alloy from the liquid state, the  temperature drops continuously till liquidus point, a , at which crystals of proeutectic α begins to form. On further cooling the fraction of α increases. At a point, b , in  the two-phase region the α fraction is given by the lever rule as bn/mn . 67

Eutectic Cooling Curves Solidification of proeutectic α continues till the eutectic  temperature is reached. The inflection in the cooling curve between points a and e is due to evolution of the latent heat. At the eutectic point ( e ) the solidification of eutectic mixture ( α  + β ) begins through the eutectic reaction and proceeds at a constant temperature as F = 0 (2 – 3 + 1). The cooling behavior in hypereutectic alloy is similar except that  proeutectic β forms below the liquidus. For a eutectic composition, the proeutectic portion is absent and  the cooling curve appears like that of a pure metal. Any composition left of point c or right of point d ( α and β  single phase region respectively) will cool and solidify like an isomorphous system. 68

Peritectic Cooling Curves L + α → β . An alloy cooling slowly through the peritectic point,  P , the α phase will crystallize first just below the liquidus line. At the peritectic temperature, T P all of the liquid and α will convert to β . Any composition  left of P will generate excess α and similarly compositions right of P will give rise to an excess of liquid. Peritectic systems –  Pt - Ag, Ni - Re, Fe - Ge, Sn - Sb (Babbitt) 69

Monotectic Cooling Curves Another three phase invariant reaction that occurs in some binary  system is monotectic reaction in which a liquid transforms to another liquid and a solid. L 1 → L 2 + α . T wo liquids are immiscible like water and oil over certain range  of compositions. Cu–Pb system has a monotectic at 36 % Pb and 955  C. 70

Phase Diagrams with Intermediate Phases Binary systems can have two types of solid solutions/phases  – terminal phases and intermediate phases . T erminal phases occur near the pure metal ends, e.g. α and β  phases in the eutectic system. Intermediate phases occur inside the phase diagram and are  separated by two-phase regions. The Cu-Zn system contains both types of phases. α and  are  terminal phases and β ,  ,  , and  are intermediate phases. Intermediate phases form in ceramic phase diagrams also. For  example, in the Al 2 O 3 – SiO 2 system an intermediate phase called mullite (3Al 2 O 3 .2SiO 2 ) is formed. 71

Phase Diagrams with Compounds Sometimes a crystalline compound called intermetallic  compound may form between two metals. Such compounds generally have a distinct chemical formula or  stoichiometry. Example – Mg 2 Pb in the Mg-Pb system (appear as a vertical line  at 81 wt.% Pb ), Mg 2 Ni, Mg 2 Si, Fe 3 C. 72 Mg - Pb phase diagram

Phase Diagrams with Compounds Properties and Applications of Intermetallics Intermetallics such as Ti 3 Al and Ni 3 Al have an ordered crystal structure where  the Ti and Al atoms occupy specific locations in the crystal rather than random locations as in most solid solutions. In TiAl the Ti atoms are located at the corner and the top and bottom faces of  the unit cell whereas Al atoms are only at the other four faces of the unit cell. This ordered structure makes it difficult for dislocations to move, which results  in poor ductility at low temperatures, which increases at high temperatures. TiAl also has a high activation energy for diffusion, giving good creep  resistance at elevated temperatures. The unit cell of two intermetallic compounds: a) TiAl has an ordered tetragonal structure and b) Ni 3 Al has an ordered cubic structure. 73

Example Point C has a composition 60 wt.% Pb alloy and at 150  C. a) What are the phases present? b) What are the compositions of the phases present? c) Mass fraction? d) Volume fraction? Knowing that the densities of Pb and Sn are 11.23 and 7.24 g/cm 3 , respectively 74

Example 75

Phase Diagrams Containing Three-Phase Reactions In the more complex binary phase diagrams, the type of melting  is sometimes used to describe the type of intermediate that occurs along with a particular type of solid state reaction Congruently melting compounds are those that maintain their  specific composition right up to the melting point. This appears as a localized “dome” in the liquidus region of the phase diagram Incongruent melting compounds do not occur directly from the  liquidus, but are formed by some form of solid-state reaction The five most common three-phase reactions that occur in phase  diagrams are:  Eutectic – a liquid transforming into two new solids on cooling  Peritectic – a liquid plus a solid transforms into a new solid  Monotectic – a liquid transforms into a new liquid and a solid  Eutectoid – a solid transforms into two new solids  Peritectoid – two solids transforms into a new solid 76

Phase Diagrams Containing Three-Phase Reactions Three phase reaction type, reaction equation and appearance on a phase diagram 77

Phase Diagrams Containing Three-Phase Reactions Above Below T ype Homotectic L L' + L “ Monotectic L L' + S Eutectic Eutectic L S 1 + S 2 Catatectic S 1 S 2 + L Monotectoid S 1 S' 1 + S 2 Eutectoid Eutectoid S 1 S 2 + S 3 Syntectic L + L ‘ S Peritectic Peritectic L + S 1 S 2 Peritectoid S 1 + S 2 S 3 Peritectoid Three phase reaction types and reaction equations 78

RULES OF THREE PHASE REACTIONS  Locate a horizontal line (isotherm) on the phase diagram. The horizontal line, which indicates the presence of a three-phase reaction, represents the temperature at which the reaction occurs under equilibrium conditions  Locate three distinct points on the horizontal line: the two end points plus a third point. The center point represents the composition at which the three-phase reaction occurs  Write in reaction form the phase(s) above the center point transforming to the phase(s) below the point. In most cases the reaction will be a eutectic, eutectoid, peritectic, etc. 79

Development of Microstructure in Eutectic Alloys • Cooling of liquid lead/tin system at different compositions. • Several types of microstructures forms during slow cooling at different compositions. 80

Development of Microstructure in Eutectic Alloys  C o less than 2 wt.% Sn  In this case of lead – rich alloy (0 – 2 wt.% of tin) solidification proceeds in the same manner as for isomorphous alloys (e.g. Cu – Ni) that was discussed earlier.  Result o at extreme ends o polycrystals of α grains i.e. only one solid phase 81

Development of Microstructure in Eutectic Alloys Alloys that exceed the solubility limit • Pb – Sn alloys between 2 – 19 wt.% Sn also solidify to produce a single solid solution, however, as the solid- state reaction continues, a second solid phase, β , precipitates from the α phase. • The solubility of Sn in solid Pb at any temperature is given by the solvus curve. • Any alloy containing between 2% – 19 % Sn that cools past the solvus exceeds the solubility resulting in the precipitation of the β phase. 82

Development of Microstructure in Eutectic Alloys • 2 wt.% Sn < C o < 19 wt.% Sn • Result o initially liquid + α o then α alone o finally two phases  α polycrystals  fine β phase inclusions 83

Development of Microstructure in Eutectic Alloys Alloys that exceed the solubility limit • The Pb – 61.9 wt.% Sn alloy has the eutectic composition. • The eutectic composition has the lowest melting temperature. • The eutectic composition has no freezing range as solidification occurs at one temperature (183  C in the Pb - Sn alloy). • The Pb - Sn eutectic reaction forms two solid solutions and is given by: L 61.9 % Sn → α 19 % Sn + β 97.5% Sn 84 • The compositions are given by the ends of the eutectic line.

Development of Microstructure in Eutectic Alloys • C o = C E • Result o eutectic microstructure (lamellar structure) i.e. alternating layers (lamellar) of α and β phases • The Pb - Sn eutectic reaction : L 61.9 % Sn → α 19 % Sn + β 97.5% Sn 85

Development of Microstructure in Eutectic Alloys a) Atom redistribution during Cooling curve for a lamellar growth of a Pb-Sn eutectic alloy is a simple eutectic. Sn atoms from the thermal arrest, since liquid preferentially diffuse to the eutectics freeze or melt at  plates, and Pb atoms diffuse to a single temperature. the  plates. b) Photograph of the Pb-Sn eutectic. 86

Development of Microstructure in Eutectic Alloys Hypoeutectic Alloy • This is an alloy whose composition will be between the left- hand-side of the end of the tie line and the eutectic composition. • For the Pb-Sn alloy, it is between 19 wt.% and 61.9 wt.% Sn. • In the hypoeutectic alloy, the liquid solidifies at the liquidus temperature producing solid, α and is completed by going through the eutectic reaction. 87

Development of Microstructure in Eutectic Alloys Hypoeutectic Alloy  19 wt.% Sn < C o < 61.9 wt.% Sn  Result o initially liquid + α o then α and eutectic microstructure  Just above T E : C α = 19 wt.% Sn and C β = 61.9 wt.% Sn � � �  Just below T E : C α = 19 wt.% Sn and C β = 97.5 wt.% Sn � 88 � �

Development of Microstructure in Eutectic Alloys Hypereutectic Alloy • This is an alloy whose composition will be between the right- hand-side of the end of the tie line and the eutectic composition. • For the Pb-Sn alloy, it is between 61.9 % and 97.5 % Sn. • The primary or proeutectic solid that forms before the eutectic phase is the  phase which is different from the eutectic solid a) A hypereutectic alloy of Pb-Sn and b) a hypoeutectic and leads to a variation alloy of Pb-Sn where the dark constituent is the Pb-rich α in microstructure. phase and the light constituent is the Sn-rich β phase and 89 the fine plate structure is the eutectic.

Hypoeutectic and Hypereutectic 90

Strength of Eutectic Alloys • Some eutectics can be strengthened by cold working. • Adding grain refiners, or inoculants, during solidification can decrease grain size. • The amount and microstructure of the eutectic can also be controlled. • Each eutectic colony can nucleate and grow independently having the orientation of the lamellae being identical. Colonies in the Pb-Sn eutectic and the effect of growth rate, R, on the interlamellar spacing, l , in the eutectic, which follows the relationship:  l  cR 1 / 2 91

Strength of Eutectic Alloys  The lamellae orientation changes on crossing from one colony boundary to another.  By refining the colony size by inoculation, the strength can be improved.  The eutectic is strengthened by decreasing the interlamellar spacing. Interlamellar spacing  This is the distance between the center of one α lamella to the center of the next α lamella.  A small interlamellar spacing indicates that the amount of  → β interface area is large. The interlamellar  A small interlamellar spacing therefore spacing in a eutectic increases the strength of the eutectic. microstructure. 92

Microstructure of Eutectic Alloys  Not all eutectics give a lamellar structure.  The morphology of the two phases depends on the cooling rate, presence of impurities, and the nature of the alloy.  An example is a Al-Si alloy where the Si portion of the eutectic grows as thin platelets (much have a high surface interface energy) growing as thin, flat platelets, which concentrate stresses leading to reduced ductility and toughness.  Modification causes the Si phase to grow as thin, interconnected rods between dendrites of Al, which increases strength and elongation. T ypical eutectic microstructures of Al-Si where a) shows needle-like plates and b) shows a modified structure of rounded rods 93

Microstructure of Eutectic Alloys If the alloys cools too quickly, a non-equilibrium solidus curve is produced.  Example, for a Pb-15 wt.% Sn alloy, the  phase should freeze at 230  C,  which is well above the eutectic temperature of 183  C. As the α phase continues to grow until, just above 183  C, the remaining  non-equilibrium liquid contains 61.9 wt.% Sn, the eutectic composition. This liquid then transforms to the eutectic microconstituent, surrounding the  primary α phase. For the conditions shown in the figure below, the amount of eutectic is:  15 10    % eutectic 100 9 . 6 %  61 . 9 10 At near equilibrium conditions, 100 % α phase should form. For non-equilibrium solidification a microstructure of α phase and a eutectic microconstituent form if the solidification is too rapid. 94

Peritectic Cooling Curves L + β → α . An alloy cooling slowly through the peritectic point,  P , the β phase will crystallize first just below the liquidus line. At the peritectic temperature, T P all of the liquid and β will convert to α . Any composition  left of P will generate excess β and similarly compositions right of P will give rise to an excess of liquid. Peritectic systems –  Pt - Ag, Ni - Re, Fe - Ge, Sn - Sb (Babbitt) 95

The Iron – iron Carbide (Fe-Fe 3 C) Phase Diagram In their simplest form, steels are alloys of Fe and C. The Fe-C phase diagram is a fairly complex one, but we will consider the steel and cast iron part of the diagram, up to around 6.70 wt% C. 96

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Phases in Fe-Fe 3 C Phase Diagram 1. α -ferrite – solid solution of C in BCC Fe Stable form of iron at room temperature • The maximum solubility of C is 0.022 wt.% • T ransforms to FCC γ -austenite at 912 o C • 2. γ -austenite – solid solution of C in FCC Fe The maximum solubility of C is 2.14 wt.% • T ransforms to BCC δ -ferrite at 1395 o C • Is not stable below the eutectoid temperature (727 o C) unless • cooled rapidly 3. δ -ferrite – solid solution of C in BCC Fe • The same structure as α -ferrite • Stable only at high T , above 1394 o C • Melts at 1538 o C 4. Fe 3 C (iron carbide or cementite) This intermetallic compound is metastable, it remains as a • compound indefinitely at room T , but decomposes (very slowly, within several years) into α -Fe and C (graphite) at 650-700 o C 5. Fe-C liquid solution 98

Phases in Fe-Fe 3 C Phase Diagram The following phases are involved in the transformation, occurring with iron-carbon alloys: L – Liquid solution of carbon in iron  δ -ferrite – Solid solution of carbon in iron. Maximum  concentration of carbon in δ -ferrite is 0.09 wt.% C at 1493  C – temperature of the peritectic transformation. The crystal structure of δ -ferrite is BCC. Austenite –interstitial solid solution of carbon in in  -iron.  Austenite has FCC crytal structure, permitting high solubility of carbon – up to 2.06 wt.% C at 1147  C and maximum carbon concentration at this temperature is 0.83 wt.% C. α -ferrite – solid solution of carbon in α -iron. Α -ferrite has BCC  crystal structure and low solubility of carbon – up to 0.25 wt.% C at 723  C. α -ferrite exists at room temperature. Cementite – iron carbide, intermetallic compound, having fixed  composition Fe 3 C. 99

Iron – Iron Carbide (Fe-Fe 3 C) Phase Diagram Phase Compositions at Room T emperature  Hypoeutectoid steels (carbon content from 0.025 to 0.83 wt.% C) consist of primary (proeutectoid) ferrite and pearlite  Eutectoid steel (carbon content of 0.83 wt.% C) consists of pearlite  Hypereutectoid steels (carbon content from 0.83 wt.% C to 2.14 wt.% C) consist of primary (proeutectoid) cementite and pearlite  Cast iron (carbon content from 2.14 wt.% C) consist of proeutectoid cementite ejected from austenite according to the curve ACM, pearlite and transformed ledeburite (ledeburite in which austenite transformed to pearlite). 100