preparation of materials n.
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  2. 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. MSEC-PHY-MMY

  3. Phase Diagrams • A phase diagram is a graphical representation of the phases that are present in a material at various temperatures and pressures and compositions. • It usually describes the equilibrium conditions • Sometimes non-equilibrium conditions are also shown when well known. MSEC-PHY-MMY

  4. Phase Diagram • 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. • For a pure substance, the Pressure-Temperature phase diagram simply tells which forms (solid, liquid, gas) of the material exist under different P-T conditions. Phase diagram for magnesium, showing the melting and boiling temperatures at one atmosphere pressure. Phase diagram for water. MSEC-PHY-MMY

  5. General Types of Phase Diagrams • 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 Tin and Zinc alloying additions to Copper to form bronze and brass, respectively • Interstitial alloys have elements, which are incorporated into the interstitial sites of the unit cell. • An example is carbon in iron to form steel. MSEC-PHY-MMY

  6. Gibb’s Phase Rule Gibb’s phase rule describes the thermodynamic state of a material. This famous rule is used to determine the number of phases that can coexist in equilibrium in a given system. It has the general form: F = C – P + 2 C is the number of components, usually elements or compounds, in the system. F is the number of degrees of freedom, or number of variables, such as temperature, pressure, or composition that are allowed to change independently without changing the number of phases in equilibrium. P is the number of phases present The constant “2” in the equation implies that both temperature and pressure are allowed to change. MSEC-PHY-MMY

  7. Gibb’s Phase Rule • For the triple point of water: • One component, i.e., water. • 3 phases present, i.e. vapor, liquid, and solid. • F = 1 – 3 + 2 = 0, so this is an invariant point on the diagram • Most binary phase diagrams used in materials science are temperature and composition diagrams at a constant 1 atmosphere of pressure. • The constant pressure will reduce the degrees of freedom from “2” in Gibb’s equation to “1” for a binary phase diagram • Thus, F = C – P + 1. MSEC-PHY-MMY

  8. Liquidus/Solidus Temperatures The liquidus temperature is the temperature above which a material is completely liquid. The solidus temperature is the temperature 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, ie., the liquid and solid. The cooling curve for an isomorphous alloy during solidification. The changes in slope of the cooling curve indicate the liquidus and solidus temperatures. This is the Mech 285 Solidification Lab. MSEC-PHY-MMY

  9. Tie Line A binary phase diagram between two elements A and B. 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 Gibbs phase rule, which provides for only one degree of freedom. MSEC-PHY-MMY

  10. Lever Rule • 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!) • In general: • Phase percent = opposite arm of lever x 100 • total length of the tie line • For example, MSEC-PHY-MMY

  11. Lever Rule When a material solidifies it does not have a constant concentration throughout the material but there will be concentration gradients, which will significantly alter the properties of the material. This is an important concept. In the example of Cu and Ni, the concentration of Ni that freezes at 1270 oC is 50 wt%, at 1250 oC is 45 wt% and 1200 oC is 40 wt%. MSEC-PHY-MMY

  12. Lever Rule • Calculate the amount of a phase and L phase present in a Cu - 40% Ni alloy at 1250 C • In general: • Percent a phase = (% Ni in alloy) – (% Ni in L) x 100 • % Ni in L - % Ni in a MSEC-PHY-MMY

  13. Solidification of a Solid-Solution Alloy The change in structure and composition of a Cu-40% Ni alloy during equilibrium solidification showing that the liquid contains 40% Ni and the first solid contains Cu-52% Ni. At 1250 C, solidification has advanced and the phase diagram tells us that the liquid contains 32% Ni and the solid contains 45% Ni, which continues until just below the solidus, all of the solid contains 40% Ni, which is achieved through diffusion. MSEC-PHY-MMY

  14. Nonequilibrium Solidification and Segregation When cooling is too fast for atoms to diffuse and produce equilibrium conditions, nonequilibriumconcentrations 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. MSEC-PHY-MMY

  15. 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. MSEC-PHY-MMY

  16. Microsegregation and Homogenization 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. MSEC-PHY-MMY

  17. Phase Diagrams with Intermediate Phases and Compounds • Many combinations of two elements produce more complicated phase diagrams than the isomorphous systems and the simple eutectic systems. • Many equilibrium diagrams often show intermediate phases and compounds when either incomplete solubility or compound formation occurs. • These new phases are distinguished by the labels “terminal phases” and “intermediate phases”. • Their phase diagrams look complex. MSEC-PHY-MMY

  18. Phase Diagrams with Intermediate Phases and Compounds • The terminal solid-solution phases occur at the ends of the phase diagrams, bordering on the pure components, e.g., the alpha phase and the beta phase in the Pb-Sn phase diagram. • Intermediate phases commonly have new compounds and are called intermediate compounds or intermetallic compounds. • An intermediate compound is made up of two or more elements that produce a new phase with its owncomposition, crystal structure, and properties. • Intermediate compounds are almost always veryhard and brittle. • An example is Fe3C in steels. MSEC-PHY-MMY

  19. In more complex phase diagrams, the type of melting is sometimes used to describe the type of intermediate compound 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 important three-phase reactions that occur in phase diagrams are: • Eutectic – a liquid transforms into two solids upon cooling • Eutectoid – a solid transforms into two new solids • Peritectic – a liquid plus a solid transforms into a new solid • Peritectoid – two solids transforms into a new solid • Monotectic – a liquid transforms into a new liquid and a solid. Phase Diagrams Containing Three-Phase Reactions MSEC-PHY-MMY

  20. Three phase reaction type, reaction equation and appearance on a phase diagram. MSEC-PHY-MMY

  21. Isomorphous Phase Diagrams A phase diagram shows the phases and their compositions at any combination of temperature and alloy composition 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 %. MSEC-PHY-MMY

  22. 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. Eutectic Phase Diagrams Solidification and microstructure of Pb-Sn alloy showing single-phase solid solution at 2 wt%. MSEC-PHY-MMY

  23. Alloys that exceed the solubility limit • Pb-Sn alloys between 2% - 29% Sn also solidify to produce a single solid solution, however, as the solid-state reaction continues, a second solid phase, b, precipitates from the a phase. • The solubility of Sn in solid Pb at any temperature is given by the solvuscurve. We’ll see later how this is important for age hardening materials. • Any alloy containing between 2% and 19% Sn that cools past the solvus exceeds the solubility resulting in the precipitation of the b phase. Eutectic Phase Diagrams Solidificaton, precipitation and microstructure of Pb-10%Sn alloy. Some dispersion strengthening occurs as the b solid precipitates. MSEC-PHY-MMY

  24. Alloys that exceed the solubility limit • The Pb – 61.9% 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a19% Sn + b97.5% Sn • The compositions are given by the ends of the eutectic line. Eutectic Phase Diagrams Solidificaton and microstructure of eutectic alloy of Pb-61.9%Sn. Often eutectic alloys have a special microstructure as shown. MSEC-PHY-MMY

  25. Eutectic Phase Diagrams a) Atom redistribution during lamellar growth of a Pb-Sn eutectic. Sn atoms from the liquid preferentially diffuse to the b plates, and Pb atoms diffuse to the a plates. b) photograph of the Pb-Sn eutectic. Cooling curve for a eutectic alloy is a simple thermal arrest, since eutectics freeze or melt at a single temperature. Review example 11-4 in Askeland and Phule, which shows you how to calculate the amount and composition of eutectic phases. MSEC-PHY-MMY

  26. Eutectic Phase Diagrams • Hypoeutectic alloy • This is an alloy whose composition will be between the left-hand-sideof the end of the tie line and the eutectic composition. • For the Pb-Sn alloy, it is between 19% and 61.9% Sn. • In the hypoeutectic alloy, the liquid solidifies at the liquidus temperature producing solid, a and is completed by going through the eutectic reaction. Solidificaton and microstructure of a hypoeutectic alloy of Pb-30%Sn. MSEC-PHY-MMY