MSE 260: Phase Transformations PDF

MSE 260: PHASE TRANSFORMATIONS (2 credits) 2nd Semester, 2023/2024 Academic Year Department of Materials Engineering. Kwame Nkrumah University of Science and Technology. Daniel N. Ampong [email protected] +233 55 304 1496 (...

MSE 260: PHASE TRANSFORMATIONS (2 credits) 2nd Semester, 2023/2024 Academic Year Department of Materials Engineering. Kwame Nkrumah University of Science and Technology. Daniel N. Ampong [email protected] +233 55 304 1496 (whatsApp) Rm # HA Area 1  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 temperatures. 2  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 3  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 %. 4  Isomorphous Systems Systems With Complete Solid Solution Plagioclase (Ab-An, NaAlSiO8 - CaAl2Si2O8) 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. 5  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!) Co ▪ In general: 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑟𝑚 𝑜𝑓 𝑙𝑒𝑣𝑒𝑟 𝑃ℎ𝑎𝑠𝑒 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 = 𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑖𝑒 𝑙𝑖𝑛𝑒 ▪ Example, for the liquid – solid (CL – CS) region, the weight fractions of ▪ When an alloy is present in a 𝐶𝑂 − 𝐶𝐿 two phase region, a tie line at 𝑋𝑠 = 𝐶𝑆 − 𝐶𝐿 the temperature of interest fixes the composition of the two 𝐶𝑆 − 𝐶𝑂 phases. 𝑋𝑙 = 𝐶𝑆 − 𝐶𝐿 ▪ This is a consequence of the where CL = the liquid composition, Gibbs phase rule, which CS = the solid composition, and provides for only one degree of freedom. CO = the bulk composition 6 Determination of Phase(s) Present Rule 1: If we know T and Co, then we must know: ❖ how many phases and which phases are present. Example: Melting points: Cu = 1085 °C Ni = 1453 °C A (1100 C, 60 wt.% Ni): 1 phase: α B (1250 C, 35 wt.% Ni): 2 phases: L + α Cu-Ni system 7  Composition of Phase(s) Rule 2: If we know T and Co, then we must know: ❖ the composition of each phase Example: At TA = 1320 C Only liquid (L) present CL = C0 (35 wt.% Ni) At TD = 1190 C Only solid (α) present Cα = C0 (35 wt.% Ni) At TB = 1250 C Both α and L present CL = Cliquidus (32 wt.% Ni) Cα = Csolidus (43 wt.% Ni) Cu-Ni system 8  Weight Fraction of Phase(s) Rule 3: If we know T and Co, then we must know: ❖ the amount of each phase (given in wt.%) Example: Co = 35 wt.% Ni At TA = Only liquid (L) WL = 100 wt.%, Wα = 0 At TD = Only solid (α) WL = 0, Wα = 100 wt.% At TB = Both α and L 𝐶𝛼 − 𝐶𝑜 43 −35 WL = = = 73 𝑤𝑡. % 𝐶𝛼 − 𝐶𝐿 43 −32 𝐶𝑜 − 𝐶𝐿 35 −32 Wα = = = 27 𝑤𝑡. % 𝐶𝛼 − 𝐶𝐿 43 −32 Cu-Ni system 9  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 10 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. 11 Cored vs Equilimbrium Phases 12  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 composition to be evened out 13  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). 14 Mechanical Properties: Cu – Ni System 15  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. 16  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. 17  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 are called solvus lines. 18  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. 19  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. 20  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. 21  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. 22  Peritectic Cooling Curves ▪ L + β → α. An alloy cooling slowly through the peritectic point, P, the α phase will crystallize first just below the liquidus line. At the peritectic temperature, TP all of the liquid and β will convert to α. ▪ 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) 23  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. L1 → L2 + α. ▪ Two liquids are immiscible like water and oil over certain range of compositions. Cu–Pb system has a monotectic at 36 % Pb and 955 C. 24  Phase Diagrams with Intermediate Phases ▪ Binary systems can have two types of solid solutions/phases – terminal phases and intermediate phases. ▪ Terminal 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 Al2O3 – SiO2 system an intermediate phase called mullite (3Al2O3.2SiO2) is formed. 25  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 – Mg2Pb in the Mg-Pb system (appear as a vertical line at 81 wt.% Pb ), Mg2Ni, Mg2Si, Fe3C. Mg - Pb phase diagram 27  Phase Diagrams with Compounds Properties and Applications of Intermetallics ▪ Intermetallics such as Ti3Al and Ni3Al 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) Ni3Al has an ordered cubic structure. 28  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/cm3, respectively 29 Example 30  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 31 Phase Diagrams Containing Three-Phase Reactions Three phase reaction type, reaction equation and appearance on a phase diagram 32 Phase Diagrams Containing Three-Phase Reactions Above Below Type Homotectic L L' + L“ Monotectic L L' + S Eutectic Eutectic L S1 + S2 Catatectic S1 S2 + L Monotectoid S1 S'1 + S2 Eutectoid Eutectoid S1 S2 + S3 Syntectic L + L‘ S Peritectic Peritectic L + S1 S2 Peritectoid S1 + S2 S3 Peritectoid Three phase reaction types and reaction equations 33 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 endpoints plus a third point. The center point represents the composition at which the three-phase reaction occurs ▪ Write the reaction that forms the phase(s) above the center point transforming to the phase(s) below the point. In most cases, the reaction will be a eutectic, 34 eutectoid, peritectic, etc.  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. 35  Development of Microstructure in Eutectic Alloys ▪ Co 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 36  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. 37 Development of Microstructure in Eutectic Alloys 2 wt.% Sn < Co < 19 wt.% Sn Result o initially liquid + α o then α alone o finally two phases ❖ α polycrystals ❖ fine β phase inclusions 38  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: L61.9 % Sn → α19 % Sn + β 97.5% Sn The compositions are given by the ends of the eutectic line. 39 Development of Microstructure in Eutectic Alloys Co = CE Result o eutectic microstructure (lamellar structure) i.e. alternating layers (lamellar) of α and β phases The Pb - Sn eutectic reaction : L61.9 % Sn → α19 % Sn + β 97.5% Sn 40 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. 41  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. 42  Development of Microstructure in Eutectic Alloys Hypoeutectic Alloy ▪ 19 wt.% Sn < Co < 61.9 wt.% Sn ▪ Result o initially liquid + α o then α and eutectic microstructure ▪ Just above TE: Cα = 19 wt.% Sn and CL = 61.9 wt.% Sn 𝑹 40 − 19 𝑊𝐿 = = = 49% 𝑹 + 𝑺 61.9 − 19 𝑊𝛼 = 100 − 𝑊𝐿 = 51% ▪ Just below TE: Cα = 19 wt.% Sn and Cβ = 97.5 wt.% Sn 𝑹 40 − 19 𝑊𝛽 = = = 27% 𝑹 + 𝑺 97.5 − 19 𝑊𝛼 = 1 − 𝑊 = 73% 43  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 44 and Hypoeutectic and Hypereutectic 45