Chapter 9 phase diagrams 1
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The document provides information on phase diagrams, including definitions of key concepts like phases, phase equilibria, and binary phase diagrams. It discusses one-component and binary systems, focusing on isomorphous, eutectic, and iron-carbon systems. For binary systems, it explains how to interpret phase diagrams to determine the phases present, phase compositions, and phase amounts using rules like lever rule. It summarizes common reactions like eutectic, eutectoid, and peritectic and analyzes the iron-carbon phase diagram in detail.
Chapter 9 phase diagrams 1
- 1. Phase Diagrams Chapter reading 9 Definitions and basic concepts Phases and microstructure Phase equilibria One component phase diagrams Binary phase diagrams The iron-carbon system (steel and cast iron) MSE-211-Engineering Materials 1 1 1
- 2. Phase Diagrams Background/Importance Many material systems and alloy systems exist in more than one phases depending on the conditions of temperature, pressure and compositions. Each phase will have different microstructure which is related to the mechanical properties. The development of microstructure is related to the characteristics of phase diagrams. Thus the knowledge and understanding of the phase diagrams is very important for engineers . Proper knowledge and understanding of phase diagrams will lead to design and control of heating procedures for developing the required microstructure and properties. MSE-211-Engineering Materials 2
- 3. Definitions and basic concepts Component - chemically recognizable species (Fe and C in carbon steel, H2O and NaCl in salted water). A binary alloy contains two components, a ternary alloy – three, etc. The chemical elements which make up the alloy Solvent : primary atomic species. Host atoms Solute : the impurities. Normally the minor component System : Specific body of material under consideration (e.g., a ladle of molten steel) MSE-211-Engineering Materials 3
- 4. Definitions and basic concepts Solubility limit: Maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution. Example : water-sugar solution Sugar/Water Phase Diagram Solubility Limit 80 What is the solubility limit for sugar in water at 20 ºC Ans: 65 wt% sugar L (liquid) 60 L 40 (liquid solution i.e., syrup) 0 + S (solid sugar) At 20ºC, if C < 65 wt% sugar: syrup At 20ºC, if C > 65 wt% sugar: syrup + sugar 20 40 60 65 80 100 C = Composition (wt% sugar) Sugar 20 Water Temperature (ºC) 10 0 MSE-211-Engineering Materials 4
- 5. Definitions and basic concepts Phase (solid, liquid, gas): a homogeneous portion of a system that has uniform physical and chemical characteristics. Two distinct phases in a system have distinct physical or chemical characteristics (e.g. water and ice) and are separated from each other by definite phase boundaries. A phase may contain one or more components. A single-phase system is called homogeneous, Systems with two or more phases are mixtures or heterogeneous systems. MSE-211-Engineering Materials 5
- 6. Effect of Temperature & Composition • Altering T can change # of phases: path A to B. • Altering C can change # of phases: path B to D. B (100ºC,C = 70) D (100ºC,C = 90) 1 phase watersugar system Adapted from Fig. 9.1, Callister & Rethwisch 8e. Temperature (ºC) 100 L 80 60 40 (liquid) L + S i.e., syrup) (solid sugar) (liquid solution 20 00 2 phases A (20ºC,C = 70) 2 phases 20 40 60 70 80 100 C = Composition (wt% sugar) MSE-211-Engineering Materials 6
- 7. Phase Equilibrium Equilibrium A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition. On a macroscopic sense this means the system is stable and its characteristics donot change over time. Under conditions of a constant temperature and pressure and composition, the direction of any spontaneous change is toward a lower free energy. MSE-211-Engineering Materials 7
- 8. Phase Equilibrium Metastable state: Equilibrium is the state that is achieved given sufficient time. It is often the case in solid systems that they never achieve complete equilibrium state because the rate to approach equilibrium is extremely slow; such a system is said to be in a non-equilibrium or metastable state. A system at a metastable state is trapped in a local minimum of free energy that is not the global one. A metastable state or microstructure may persist indefinitely, experiencing only extremely slight and almost negligible changes as time progresses. Often, metastable structures are of more practical significance than equilibrium ones. MSE-211-Engineering Materials 8
- 9. Phase Diagrams Phase Diagram–a graphic representation showing the phase or phases present for a given composition, temperature and pressure. Also termed equilibrium diagrams. A phase diagrams show what phases exist at equilibrium and what phase transformations we can expect when we change one of the parameters of the system (T, P, composition). We will discuss phase diagrams for binary alloys only and will assume pressure to be constant at one atmosphere. Phase diagrams for materials with more than two components are complex and difficult to represent MSE-211-Engineering Materials 9
- 10. ONE-COMPONENT (OR UNARY) PHASE DIAGRAMS Example of water: Three different phases. Phase boundaries: aO, bO, cO. The two phases on either side of the boundary are in equilibrium. For details Read page 86-87 MSE-211-Engineering Materials 10
- 11. Unary Systems Single component system Consider 2 elemental metals separately: Cu has melting T = 1085oC (at standard P = 1 atm) Ni has melting T = 1453oC What happens when Cu and Ni are mixed? MSE-211-Engineering Materials 11
- 12. Binary Isomorphous Systems Binary: 2 components Isomorphous system - complete solid solubility of the two components (both in the liquid and solid phases). 3 different phase fields Liquid(L) Solid + liquid(L + α) Solid(α) Liquidus line separates liquid from liquid + solid Solidus line separates solid from liquid + solid MSE-211-Engineering Materials 12
- 13. Binary Isomorphous Systems Example of isomorphous system: Cu-Ni MSE-211-Engineering Materials 13
- 14. Binary Isomorphous Systems In one-component system melting occurs at a well-defined melting temperature. In multi-component systems melting occurs over the range of temperatures, between the solidus and liquidus lines. Solid and liquid phases are in equilibrium in this temperature range. 50/50 wt % composition in Cu-Ni melting begins at 1280 C MSE-211-Engineering Materials 14
- 15. Binary Isomorphous Systems MSE-211-Engineering Materials 15
- 16. Interpretation of Phase Diagrams From binary phase diagrams we can determine (1) The phases that are present (2) The composition of phases (3) The percentage and fraction of the phases MSE-211-Engineering Materials 16
- 17. Determination of Phases Present • Rule 1: If we know T and Co, then we know: -- which phase(s) is (are) present. A(1100ºC, 60 wt% Ni): 1 phase: a B (1250ºC, 35 wt% Ni): 2 phases: L + a 1600 L (liquid) B (1250ºC,35) • Examples: T(ºC) 1500 1400 1300 Cu-Ni phase diagram a 1200 A(1100ºC,60) 1100 1000 0 20 40 MSE-211-Engineering Materials 60 80 100 wt% Ni 17
- 18. Determination of Phase Composition Finding the composition in a two phase region: 1. Locate composition and temperature in diagram 2. In two phase region draw the tie line or isotherm 3. Note intersection with phase boundaries. Read compositions at the intersections. The liquid and solid phases have these compositions. MSE-211-Engineering Materials 18
- 19. Determination of Phase Composition Point B: T=1250 oC ,35 wt% Ni– 65 wt% Cu Composition of Liquid phase: CL=31.5wt% Ni –68.5%Cu Composition of α phase: Cα=42.5wt% Ni‐57.5wt%Cu MSE-211-Engineering Materials 19
- 20. Determination of Phase Amounts Phase weight fractions or % For single phase weight fraction of a phase is 1 or 100%. For two phase region Lever Rule Locate composition and temperature in diagram Construct a tie line in two phase region at alloy temperature Fraction of a phase is determined by taking the length of the tie line from the overall alloy composition to the phase boundary for the other phase, and dividing by the total length of tie line. MSE-211-Engineering Materials 20
- 21. Determination of Phase Amounts Mass Fraction 𝐶 𝑜 = 35 𝑤𝑡. %, 𝐶 𝐿 = 31.5 𝑤𝑡. % 𝐶 𝛼 = 42.5𝑤𝑡. %, 𝑊 𝐿 = 𝐶 𝛼 − 𝐶 𝑜 𝐶 𝛼 − 𝐶 𝐿 = 0.68 𝑊𝛼 = 𝐶 𝑜 − 𝐶 𝐿 𝐶 𝛼 − 𝐶 𝐿 = 0.32 MSE-211-Engineering Materials 21
- 22. Development of microstructure in isomorphous alloys Equilibrium Cooling: Very slow cooling to allow phase equilibrium to be maintained during the cooling process. MSE-211-Engineering Materials 22
- 24. Mechanical Properties of Isomorphous Alloys Solid solution strengthening -- Ductility (%EL) 400 TS for pure Ni 300 TS for pure Cu 200 0 20 40 Cu 60 80 100 Ni Composition, wt% Ni Elongation (%EL) Tensile Strength (MPa) -- Tensile strength (TS) 60 %EL for pure Cu %EL for pure Ni 50 40 30 20 0 20 Cu MSE-211-Engineering Materials 40 60 80 100 Ni Composition, wt% Ni 2424
- 25. Binary Eutectic Systems Eutectic Systems In a eutectic reaction, when a liquid solution of fixed composition, soldifies at a constant temperature, forms a mixture of two or more solid phases without an intermediate pasty stage. This process reverses on heating. Systems exhibiting this behavior are known as “Eutectic systems”. In a eutectic system there is always a specific alloy , known as eutectic composition, that freezes at a lower temperature than all other compositions. At ‘eutectic temperature’, two solids form simultaneously from a single liquid phase. The eutectic temperature and composition determine a point on the phase diagram known as ‘eutectic point’. MSE-211-Engineering Materials 25
- 26. Binary Eutectic Systems Three single phase regions (α - solid solution of Ag in Cu matrix, β = solid solution of Cu in Ag marix, L - liquid) •Three two-phase regions (α + L, β +L, α +β) •Solvus line separates one solid solution from a mixture of solid solutions. The Solvus line shows limit of solubility MSE-211-Engineering Materials 26
- 27. Binary Eutectic Systems Eutectic or invariant point - Liquid and two solid phases co-exist in equilibrium at the eutectic composition CE and the eutectic temperature TE. Eutectic isotherm - the horizontal solidus line at TE. MSE-211-Engineering Materials 27
- 28. Binary Eutectic Systems Cu-Ag system T(ºC) Ex.: Cu-Ag system 1200 L (liquid) 1000 • TE : No liquid below TE • CE : Composition at temperature TE • Eutectic reaction L(CE) L(71.9 wt% Ag) TE 800 a 8.0 71.9 91.2 a+b 400 0 heating L +b b 779ºC 600 a(CaE) + b(CbE) 200 cooling L+a 20 40 60 CE 80 100 C , wt% Ag a(8.0 wt% Ag) + b(91.2 wt% Ag) MSE-211-Engineering Materials 28
- 29. Binary Eutectic Systems General Rules Eutectic reaction – transition between liquid and mixture of two solid phases, α + β at eutectic concentration CE. • The melting point of the eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek). • At most two phases can be in equilibrium within a phase field. • Three phases (L, α, β) may be in equilibrium only at a few points along the eutectic isotherm. • Single-phase regions are separated by 2-phase regions. MSE-211-Engineering Materials 29
- 30. Binary Eutectic Systems On occasion, low-melting-temperature alloys are prepared having near-eutectic compositions. A familiar example is the 60–40 solder, containing 60 wt% Sn and 40 wt% Pb. Completely melted at 185 C. Attractive as low temperature solder. MSE-211-Engineering Materials 30
- 31. Binary Eutectic Systems Compositions and relative amounts of phases are determined from the same tie lines and lever rule, as for isomorphous alloys. MSE-211-Engineering Materials 31
- 32. For a 40 wt% Sn-60 wt% Pb alloy at 150ºC, determine: -- the phases present the phase compositions MSE-211-Engineering Materials 32
- 33. Eutectic, Eutectoid and Pertectic Reactions • Eutectic - liquid transforms to two solid phases L cool a + b (For Pb-Sn, 183ºC, 61.9 wt% Sn) heat • Eutectoid – one solid phase transforms to two other solid phases intermetallic compound - cementite S2 S1+S3 cool a + Fe3C (For Fe-C, 727ºC, 0.76 wt% C) heat • Peritectic - liquid and one solid phase transform to a second solid phase S1 + L S2 +L cool heat (For Fe-C, 1493ºC, 0.16 wt% C) MSE-211-Engineering Materials 33
- 34. Eutectoid & Peritectic Cu-Zn Phase diagram Eutectoid transformation Peritectic transformation + L + MSE-211-Engineering Materials Adapted from Fig. 9.21, Callister & Rethwisch 8e. 34
- 35. Iron-Iron Carbide Phase Diagram MSE-211-Engineering Materials 35
- 36. Phases in Fe–Fe3C Phase Diagram 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% at 727 °C • Transforms to FCC γ-austenite at 912 °C γ-austenite - solid solution of C in FCC Fe • The maximum solubility of C is 2.14 wt % at 1147 °C . • Transforms to BCC δ-ferrite at 1395 °C • Is not stable below the eutectic temperature (727 ° C) unless cooled rapidly MSE-211-Engineering Materials 36
- 37. Phases in Fe–Fe3C Phase Diagram δ-ferrite solid solution of C in BCC Fe • The same structure as α-ferrite • Stable only at high T, above 1394 °C • Melts at 1538 °C Fe3C (iron carbide or cementite) Interstitial solution of Fe in C with maximum solubility of 6.67 wt% C. It is satble at room temperature. Crystalline structure is orthorhombic. Fe-C liquid solution MSE-211-Engineering Materials 37
- 38. A few comments on Fe–Fe3C system C is an interstitial impurity in Fe. It forms a solid solution with α, γ, δ phases of iron Maximum solubility in BCC α-ferrite is limited (max. 0.022 wt% at 727 °C) - BCC has relatively small interstitial positions Maximum solubility in FCC austenite is 2.14 wt% at 1147 °C - FCC has larger interstitial positions. Mechanical properties: Cementite is very hard and brittle -can strengthen steels. Ferrite and austenite are relatively soft phases. Magnetic properties: α -ferrite is magnetic below 768 °C, austenite is non-magnetic. MSE-211-Engineering Materials 38
- 39. Classification. Three types of ferrous alloys: • Iron: less than 0.008 wt % C in α−ferrite at room T • Steels: 0.008 - 2.14 wt % C (usually < 1 wt % ) α-ferrite + Fe3C at room T • Cast iron: 2.14 - 6.7 wt % (usually < 4.5 wt %) MSE-211-Engineering Materials 39
- 41. Development of Microstructure in Iron - Carbon alloys Microstructure depends on composition (carbon content) and heat treatment. Here we consider slow cooling in which equilibrium is maintained Microstructure of eutectoid steel MSE-211-Engineering Materials 41
- 42. Development of Microstructure in Iron - Carbon alloys Microstructure of eutectoid steel When alloy of eutectoid composition (0.76 wt % C) is cooled slowly it forms perlite, a lamellar or layered structure of two phases: α-ferrite and cementite (Fe3C). Mechanically, pearlite has properties intermediate to soft, ductile ferrite and hard, brittle cementite In the micrograph, the dark areas are Fe3C layers, the light phase is αferrite MSE-211-Engineering Materials 42
- 43. At room temperature steel is Ferrite with patches of Pearlite. MSE-211-Engineering Materials 43