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Chapter 9: Phase Diagrams

Chapter 9: Phase Diagrams. ISSUES TO ADDRESS. • When we combine two elements... what equilibrium state do we get?. • In particular, if we specify... --a composition (e.g., wt% Cu - wt% Ni), and --a temperature ( T ). then... 1. How many phases do we get?

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Chapter 9: Phase Diagrams

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  1. Chapter 9: Phase Diagrams ISSUES TO ADDRESS... • When we combine two elements... what equilibrium state do we get? • In particular, if we specify... --a composition (e.g., wt% Cu - wt% Ni), and --a temperature (T) then... 1. How many phases do we get? 2. What is the composition of each phase? 3. How much of each phase do we get? Phase B Phase A Nickel atom Copper atom

  2. Definitions: Componentsare pure metals and/or compounds of which an alloy is composed. For example, in a copper–zinc brass, the components are Cu and Zn. Systemit may relate to the series of possible alloys consisting of the same components, (e.g., the iron–carbon system). Solid solution consists of atoms of at least two different types; the solute atoms occupy either substitutional or interstitial positions in the solvent lattice, and the crystal structure of the solvent is maintained. Mixtures is a systems composed of two or more phases or ‘‘heterogeneous systems. Most metallic alloys, ceramic, polymeric, and composite systems are heterogeneous.

  3. Phase: is defined as a homogeneous portion of a system that has uniform physical and chemical characteristics. Every pure material is considered to be a phase; so also is every solid, liquid, and gaseous solution. For example, the sugar–water syrup solution Each has different physical properties (one is a liquid, the other is a solid); furthermore, each is different chemically (i.e., has a different chemical composition); one is virtually pure sugar, the other is a solution of H2O If more than one phase is present in a given system, each will have its own distinct properties, and a boundary separating the phases will exist across which there will be a discontinuous and abrupt change in physical and/or chemical characteristics When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient. Ex. water and ice

  4. Heterogeneous Mixturesare composed of two or more components that are: unequally (not uniformly) distributed though out the system, immiscible (won't dissolve), may be of different phase, unable to disperse through most membranes, and separable by mechanical means. There are probably more possibilities for this type of mixture than the first.

  5. Sucrose/Water Phase Diagram 10 0 Solubility L Limit 8 0 (liquid) 6 0 + L Temperature (°C) S (liquid solution 4 0 i.e., syrup) (solid 20 sugar) 0 20 40 60 80 100 65 Co =Composition (wt% sugar) Sugar Water Pure Pure Phase Equilibria: Solubility Limit • Introduction • Solutions – solid solutions, single phase • Mixtures – more than one phase • Solubility Limit: Max concentration for which only a single phase solution occurs, at specific temp Question: What is the solubility limit at 20°C? Answer: 65 wt% sugar. If Co < 65 wt% sugar: syrup If Co > 65 wt% sugar: syrup + sugar.

  6. The addition of solute in excess of this solubility limit results in the formation of another solid solution or compound that has a clearly different composition. To illustrate this concept, consider the sugar–water (C12H22O11–H2O) system. This solubility limit of sugar in water depends on the temperature of the water

  7. Components and Phases • Components: The elements or compounds which are present in the mixture (e.g., Al and Cu) • Phases: The physically and chemically distinct material regions that result (e.g., a and b). Aluminum- Copper Alloy b (lighter phase) a (darker phase)

  8. B (100°C,70) 1 phase D (100°C,90) 2 phases 100 L 80 (liquid) + 60 L S Temperature (°C) ( liquid solution (solid 40 i.e., syrup) sugar) A (20°C,70) 2 phases 20 0 0 20 40 60 70 80 100 Co =Composition (wt% sugar) Effect of T & Composition (Co) path A to B. • Changing T can change # of phases: • Changing Co can change # of phases: path B to D. water- sugar system

  9. Phase Equilibria • Free energy is a function of the internal energy of a system, and also the randomness or disorder of the atoms or molecules (or entropy). • A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition. In a macroscopic sense, this means that the characteristics of the system do notchangewith time but persist indefinitely; that is, the system is stable. • phase equilibrium, refers to equilibrium as it applies to systems in which more than one phase may exist. • Metastable: non-equilibrium state that may persist for a very long time (specially in solid systems, that a state of equilibrium is never completely achieved because the rate of approach to equilibrium is extremely slow)

  10. Phase Equilibria Simple solution system (e.g., Ni-Cu solution) • Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility. • Ni and Cu are totally miscible in all proportions.

  11. Phase Diagrams • Phase diagram gives information about the control of microstructure or phase structure of a particular alloy system is conveniently and concisely displayed (equilibrium or constitutional diagram) • There are three externally controllable parameters that will affect phase structure – temperature, pressure, and composition – and phase diagram are constructed when combinations of these parameters are plotted against one another

  12. One – component (or unary) phase diagram It is a one component system, in which composition is held constant ( i.e., the phase diagram is for a pure substance); that is means that pressure and temperature are variable. Ex. Water H2O liquid solid Triple point 0.01 vapour 0 Temp. 0.01 C Pressure(atm) -20 Temperature ( C)

  13. T(°C) • 2 phases region : 1600 L (liquid) 1500 L (liquid) a (FCC solid solution) • 3 phase fields: 1400 L a liquidus + 1300 a L + L solidus a a 1200 (FCC solid 1100 solution) 1000 wt% Ni 0 20 40 60 80 100 Phase Diagrams • Indicate phases as function of T, Co, and P. • For this course: -binary systems: just 2 components. -independent variables: T and Co (P = 1 atm is almost always used). •Phase Diagram for Cu-Ni system

  14. Ex. copper–nickel system The liquid L is a homogeneous liquid solution composed of both copper and nickel. The phase is a substitutional solid solution consisting of both Cu and Ni atoms, and having an FCC crystal structure. At temperatures below about 1080C, copper and nickel are mutually soluble in each other in the solid state for all compositions. This complete solubility is explained by the fact that both Cu and Ni have the same crystal structure (FCC), nearly identical atomic radii and electro-negativities, and similar valences. The copper–nickel system is termed isomorphous because of this complete liquid and solid solubility of the two components.

  15. T(°C) 1600 L (liquid) 1500 a 1 phase: Cu-Ni phase diagram liquidus B (1250°C, 35): (1250°C,35) 1400 solidus a 2 phases: L + a a + 1300 L B (FCC solid 1200 solution) 1100 A(1100°C,60) 1000 wt% Ni 0 20 40 60 80 100 Phase Diagrams:# and types of phases • Rule 1: If we know T and Co, then we know: --the # and types of phases present. • Examples: A(1100°C, 60):

  16. Cu-Ni system T(°C) A T C = 35 wt% Ni A o tie line liquidus L (liquid) At T = 1320°C: 1300 A a + L Only Liquid (L) B T solidus B C = C ( = 35 wt% Ni) L o a a At T = 1190°C: + D L (solid) 1200 D a Only Solid ( ) T D C = C ( = 35 wt% Ni ) a o 32 35 4 3 20 30 40 50 At T = 1250°C: C C C a B L o wt% Ni a Both and L C = C ( = 32 wt% Ni here) L liquidus C = C ( = 43 wt% Ni here) a solidus Phase Diagrams:composition of phases • Rule 2: If we know T and Co, then we know: --the composition of each phase. • Examples:

  17. Phase Diagrams:weight fractions of phases Cu-Ni system T(°C) A T C = 35 wt% Ni A o tie line liquidus L (liquid) At T : Only Liquid (L) 1300 a A + L B W = 100 wt%, W = 0 a L T solidus B S R a At T : Only Solid ( ) D a a + W = 0, W = 100 wt% L a L (solid) 1200 D T a D At T : Both and L B 32 35 4 3 20 3 0 4 0 5 0 S = WL C C C a L o wt% Ni R + S R = = 27 wt% Wa R + S • Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%). • Examples: - Composition need be specified in terms of only one of the constituents for a binary alloy

  18. T(°C) tie line liquidus L (liquid) 1300 a + M ML L B solidus T B a a + L (solid) 1200 R S S R 20 3 0 4 0 5 0 C C C a L o wt% Ni The Lever Rule • Tie line – connects the phases in equilibrium with each other - essentially an isotherm • How much of each phase? Think of it as a lever (teeter-totter)

  19. DEVELOPMENT OF MICROSTRUCTURE IN ISOMORPHOUS ALLOYS EQUILIBRIUM COOLING NONEQUILIBRIUM COOLING

  20. Ex: Cooling in a Cu-Ni Binary 1. EQUILIBRIUM COOLING T(°C) L: 35wt%Ni L (liquid) Cu-Ni system a 130 0 A + L L: 35 wt% Ni B a: 46 wt% Ni 35 46 C 32 43 D L: 32 wt% Ni 24 36 a a : 43 wt% Ni + 120 0 E L L: 24 wt% Ni a : 36 wt% Ni a (solid) 110 0 35 20 3 0 4 0 5 0 wt% Ni C o • Phase diagram: Cu-Ni system. • System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another; a phase field extends from 0 to 100 wt% Ni. • Consider Co = 35 wt%Ni.

  21. NONEQUILIBRIUM COOLING

  22. Cored vs Equilibrium Phases Uniform C : a a First to solidify: 35 wt% Ni 46 wt% Ni a Last to solidify: < 35 wt% Ni • Ca changes as we solidify. • Cu-Ni case: First a to solidify has Ca = 46 wt% Ni. Last a to solidify has Ca = 35 wt% Ni. • Fast rate of cooling: Cored structure • Slow rate of cooling: Equilibrium structure

  23. 60 %EL for pure Cu 400 %EL for 50 pure Ni TS for Elongation (%EL) 40 pure Ni Tensile Strength (MPa) 300 30 TS for pure Cu 200 20 0 20 40 60 80 100 0 20 40 60 80 100 Cu Ni Cu Ni Composition, wt% Ni Composition, wt% Ni Mechanical Properties:Cu-Ni System • Effect of solid solution strengthening on: --Tensile strength (TS) --Ductility (%EL,%AR) --Peak as a function of Co --Min. as a function of Co

  24. Binary-Eutectic Systems • Eutectic transition L(CE) (CE) + (CE) has a special composition with a min. melting T. 2 components Cu-Ag system T(°C) Ex.: Cu-Ag system 1200 • 3 single phase regions L (liquid) a, b (L, ) 1000 a L + a • Limited solubility: b L + 779°C b 800 TE a : mostly Cu 8.0 71.9 91.2 b : mostly Ag 600 • TE : No liquid below TE a + b solvus 400 • CE : Min. melting TE composition 200 80 100 0 20 40 60 CE Co , wt% Ag

  25. Binary-Eutectic Systems • Depending on composition, several different types of microstructures are possible for the slow cooling of alloys belonging to binary eutectic systems. • Ex. Lead(Pb)–tin(Sn) phase diagram • The first case is for compositions ranging between a pure component and the maximum solid solubility for that component at room temperature [20C (70F)]. • For the lead–tin system, this includes lead-rich alloys containing between 0 and about 2 wt% Sn (for the phase solid solution), and also between approximately 99 wt% Sn and pure tin (for the β phase)

  26. The second case considered is for compositions that range between the room temperature solubility limit and the maximum solid solubility at the eutectic temperature. • For the lead–tin system (Figure 10.7), these compositions extend from about 2wt%Sn to 18.3 wt%Sn (for lead-rich alloys) and from 97.8 wt%Sn to approximately 99 wt% Sn (for tin-rich alloys). • The third case involves solidification of the eutectic composition, 61.9 wt% Sn (C3 in Figure). Consider an alloy having this composition that is cooled from a temperature within the liquid-phase region (e.g., 250C) down the vertical line yy in Figure. As the temperature is lowered, no changes occur until we reach the eutectic temperature, 183C. Upon crossing the eutectic isotherm, the liquid transforms to the two and phases. This transformation may be represented by the reaction

  27. The fourth and final micro structural case for this system includes all compositions other than the eutectic that, when cooled, cross the eutectic isotherm. Consider, for example, the composition C4 , see figure, which lies to the left of the eutectic; as the temperature is lowered, we move down the line zz, beginning at point j.

  28. EX: Pb-Sn Eutectic System (1) T(°C) 300 L (liquid) a L + a b b L + 200 183°C 18.3 61.9 97.8 C- CO 150 S R S = W = a R+S C- C 100 a + b 99 - 40 59 = = = 67 wt% 99 - 11 88 100 0 11 20 60 80 99 40 CO - C R W C C Co = =  C, wt% Sn C - C R+S 40 - 11 29 = = 33 wt% = 99 - 11 88 • For a 40 wt% Sn-60 wt% Pb alloy at 150°C, find... --the phases present: a + b Pb-Sn system --compositions of phases: CO = 40 wt% Sn Ca = 11 wt% Sn Cb = 99 wt% Sn --the relative amount of each phase:

  29. EX: Pb-Sn Eutectic System (2) T(°C) CL - CO 46 - 40 = W = a CL - C 46 - 17 300 L (liquid) 6 a L + = = 21 wt% 29 220 a b b R L + S 200 183°C 100 a + b 100 17 46 0 20 40 60 80 C CL Co C, wt% Sn CO - C 23 = W = = 79 wt% L CL - C 29 • For a 40 wt% Sn-60 wt% Pb alloy at 200°C, find... --the phases present: a + L Pb-Sn system --compositions of phases: CO = 40 wt% Sn Ca = 17 wt% Sn CL = 46 wt% Sn --the relative amount of each phase:

  30. Microstructures in Eutectic Systems: I T(°C) L: Cowt% Sn 400 L a L 300 L a + a 200 (Pb-Sn a: Cowt% Sn TE System) 100 b + a 0 10 20 30 Co , wt% Sn Co 2 (room T solubility limit) • Co < 2 wt% Sn • Result: --at extreme ends --polycrystal of a grains i.e., only one solid phase.

  31. Microstructures in Eutectic Systems: II L: Co wt% Sn T(°C) 400 L L 300 a L + a a: Cowt% Sn a 200 TE a b 100 b + a Pb-Sn system 0 10 20 30 Co , wt% Sn Co 2 (sol. limit at T ) 18.3 room (sol. limit at TE) • • 2 wt% Sn < Co < 18.3 wt% Sn • • Result: • Initially liquid +  • then  alone • finally two phases • a polycrystal • fine -phase inclusions

  32. Microstructures in Eutectic Systems: III Micrograph of Pb-Sn T(°C) eutectic L: Co wt% Sn microstructure 300 L Pb-Sn system a L + a b L 200 183°C TE 100 160m a : 97.8 wt% Sn : 18.3 wt%Sn 0 20 40 60 80 100 97.8 18.3 CE C, wt% Sn 61.9 • Co = CE • Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of a and b crystals.

  33. Lamellar Eutectic Structure

  34. Microstructures in Eutectic Systems: IV • Just above TE : L T(°C) L: Co wt% Sn a C = 18.3 wt% Sn a L a CL = 61.9 wt% Sn 300 L Pb-Sn system S W a L + a = 50 wt% = R + S a b WL = (1- W ) = 50 wt% b L + a R S 200 TE S R • Just below TE : C = 18.3 wt% Sn a a b 100 + a primary C = 97.8 wt% Sn b a eutectic S b eutectic W a = 73 wt% = R + S 0 20 40 60 80 100 W = 27 wt% b 18.3 61.9 97.8 Co, wt% Sn • 18.3 wt% Sn < Co < 61.9 wt% Sn • Result:a crystals and a eutectic microstructure

  35. Hypoeutectic & Hypereutectic Hypoeutectic: alloy with a composition C to the left eutectic point (less than eutectic) Hypereutectic: alloy with a composition C to the right eutectic point (more than eutectic)

  36. Hypoeutectic & Hypereutectic hypoeutectic: Co = 50 wt% Sn hypereutectic: (illustration only) a b a b a a b b a b a b 175 mm 300 L T(°C) a L + a b b L + (Pb-Sn 200 TE System) a + b 100 Co, wt% Sn 0 20 40 60 80 100 eutectic 61.9 eutectic: Co=61.9wt% Sn 160 mm eutectic micro-constituent

  37. Intermetallic Compounds Terminal solid solution: the solid phase which exist over composition ranges near the concentration extremities. Intermediate solid solution:(or intermediate phases ) A solid solution or phase having a composition range that does not extend to either of the pure components of the system. may be found at other than the two composition extremes Intermetallic compounds: ( for metal – metal system) A compound of two metals that has a distinct chemical formula. On a phase diagram it appears as an intermediate phase that exists over a very narrow range of compositions. ; Ex. The magnesium – lead system

  38. Intermetallic Compounds Mg2Pb Note: intermetallic compound forms a line - not an area - because stoichiometry (i.e. composition) is exact.

  39. Characteristics noting for magnesium – lead system: The compound Mg2Pb melts at approximately 550 C as indicated by point M in figure The solubility of lead in magnesium is rather extensive, as indicated by the relatively large composition span for the a phase field The solubility of magnesium in lead is extremely limited. This is evident from the very narrow β terminal – solid solution region on the right or lead – rich side of the diagram This phase diagram may be thought of as two simple eutectic diagrams joined back to back, one for the Mg-Mg2Pb system and the other for Mg2Pb-Pb; as such the compound Mg2Pb is really considered to be a component

  40. cool cool cool heat heat heat • Eutectoid - solid phase transforms into two solid phases • S2S1+S3 •  + Fe3C (727ºC) intermetallic compound - cementite • Peritectic - liquid + solid 1  solid 2 (Fig 9.21) • S1 + LS2 •  + L (1493ºC) Eutectoid & Peritectic • Eutectic - liquid in equilibrium with two solids L +  Invariants point: the different phases in equilibrium ( ex. Eutectic, eutectoid, peritectic)

  41. Peritectic transition  + L Eutectoid transition  +  Eutectoid & Peritectic Cu-Zn Phase diagram

  42. THE GIBBS PHASE RULE Gibbs phase rule for construction of phase diagram Gibbs phase rule:For a system at equilibrium, an equation that expresses the relationship between the number of phases present and the number of externally controllable variables. P is the number of phases present F is the number of these variables that can be changed independently without altering the number of phases that coexist at equilibrium(T, p, C) C is the number of components in the system. N is the number of non compositional variables (e.g., temperature and pressure).(p=1atm constant, so N =1)

  43. Example: the copper–silver system Since pressure is constant (1 atm), the parameter N is 1 (temperature is the only non compositional variable) the number of components C is 2 (viz Cu and Ag), Consider the case of single-phase fields on the phase diagram (e.g., , , and liquid regions). Since only one phase is present This means that to completely describe the characteristics of any alloy that exists within one of these phase fields, we must specify two parameters; these are composition and temperature, which locate, respectively, the horizontal and vertical positions of the alloy on the phase diagram.

  44. Iron-Carbon (Fe-C) Phase Diagram • In the classification scheme of ferrous alloys based on carbon content, there are three types: iron, steel, and cast iron • Commercially pure iron contains less than 0.008 wt% C and, from the phase diagram, is composed almost exclusively of • the ferrite phase at room temperature. • 2. The iron–carbon alloys that contain between 0.008 and 2.14 • wt% C are classified as steels. In most steels the • microstructure consists of both α and Fe3C phases. • 3. Cast irons are classified as ferrous alloys that contain • between 2.14 and 6.70 wt% C. However, commercial cast • irons normally contain less than 4.5 wt% C

  45. Pure iron, upon heating, experiences two changes in crystal structure before it melts. • At room temperature the stable form, called ferrite, or αiron, has a BCC crystal structure. • At 912C (1674F ) Ferrite experiences a polymorphic transformation to FCC austenite, or iron. This austenite persists to 1394C (2541F), at which temperature the FCC austenite reverts back to a BCC phase known as  ferrite, • which finally melts at 1538C (2800F). • 3. The composition axis extends only to 6.70 wt% C; at this concentration the intermediate compound iron carbide, or cementite (Fe3C), is formed, which is represented by a vertical line on the phase diagram. Thus, the iron–carbon system may be divided into two parts: an iron-rich portion, and the other (not shown) for compositions between 6.70 and 100 wt% C (pure graphite). In practice, all steels and cast irons have carbon contents less than 6.70 wt% C;

  46. T (°C) 1600 d -Eutectic (A): L 1400 Þ g + L Fe3C g +L g A 1200 L+Fe3C 1148°C -Eutectoid (B): (austenite) R S g Þ a + Fe3C g g 1000 g +Fe3C g g a Fe3C (cementite) + 800 B g a 727°C = T eutectoid R S 600 a +Fe3C 400 0 1 2 3 4 5 6 6.7 4.30 0.76 Co, wt% C (Fe) 120 mm Fe3C (cementite-hard) Result: Pearlite = alternating layers of eutectoid a (ferrite-soft) a and Fe3C phases C Iron-Carbon (Fe-C) Phase Diagram • 2 important points

  47. The two-phase regions are labeled in Figure. 1. It may be noted that one eutectic exists for the iron–iron carbide system, at 4.30 wt% C and 1147C (2097F); for this eutectic reaction, the liquid solidifies to form austenite and cementite phases. Of course, subsequent cooling to room temperature will promote additional phase changes. 2. It may be noted that a eutectoid invariant point exists at a composition of 0.76 wt% C and a temperature of 727C (1341F). This eutectoid reaction may be represented by

  48. T (°C) 1600 d L 1400 (Fe-C g +L g g g System) 1200 L+Fe3C 1148°C (austenite) g g g 1000 g g +Fe3C g g Fe3C (cementite) r s 800 a g g 727°C a a a g g R S 600 a +Fe3C w = s /( r + s ) a w = (1- w ) g a 400 0 1 2 3 4 5 6 6.7 a Co, wt% C (Fe) C0 0.76 pearlite w = w g pearlite Hypoeutectoid 100 mm w = S /( R + S ) a steel w = (1- w ) a Fe3C pearlite proeutectoid ferrite Hypoeutectoid Steel

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