Phase Diagrams a Review Topic 2 Review of Phase Transformation Diagrams Solution and Solubility Example: Solubility of salt in water There exists a maximum amount of salt that can be completely dissolved in water; excess of salt stays as solid. This maximum amount is the solubility of salt in water. The solution containing the maximum concentration of salt is a saturated solution. Cooling of saturated solution results in the formation of solid salt from the solution, indicating that solubility decreases with decreasing T. This process is called precipitation and the solid formed is a precipitate. Heating the solution will lead to the dissolving of the Solid salt – the Salty water – precipitate back into solution. precipitate the solution In this example there exist two phases in the system and the two phases stay in equilibrium: dissolving Solution Solid precipitation The same concepts apply to solids: solid solution, saturation, solubility, precipitation Phase Diagrams phase diagram of water Phase diagrams are used to map out the existence and conditions of Super-critical Liquid various phases of a give system. fluid The phase diagram of water is a Solid common example. Water may stay Critical point in liquid, solid or gaseous states in Pressure 221 bar different pressure-temperature regions. Boundaries of the regions 1 bar express the equilibrium conditions in terms of P and T. Water is a 0 bar Gas monolithic system. For binary Triple systems, which contains two point constituents, such as binary alloys, phase diagrams are often expressed 0°C 100°C 374°C in the temperature-composition Temperature plane. Binary Phase Diagrams liquid phase - 1455°C The simplest type of binary phase Solution of diagrams is the isomorphous system, in Cu and Ni which the two constituents form a continuous solid solution over the T1 Co Temperature entire composition range. An example CS is the Ni-Cu system. T2 CL CS 1 T3 CL 2 Solidiﬁcation of alloy Co starts on Co 2 3 cooing at T1. The ﬁrst solid formed has α phase (fcc) - a composition of Cs1 and the liquid Solid solution Co. On further cooling the solid 1085°C of Cu and Ni particles grow larger in size and change their composition to Cs2 and then Co, following the solidus whereas the liquid Cu Composition Ni decrease in volume and changes its composition from Co to CL3 following L the liquidus. The solidiﬁcation α completes at T3. Binary Phase Diagrams The simplest type of binary phase liquid phase - 1455°C diagrams is the isomorphous system, in Solution of Temperature which the two constituents form a Cu and Ni Co continuous solid solution over the entire composition range. An example is the Ni-Cu system. T* CL Compositions of phases is determined CS by the tie line The relative fractions of the phases are determined by the lever rule α phase (fcc) - 1085°C Solid solution of Cu and Ni W1 W2 L1 L2 Cu Composition Ni Lever Rule W1 W2 L1 L2 Weight fractions: Example At temperature T1, alloy Co is in the dual phase region, CL CS comprising the liquid phase and the α-phase. Co (i) Determine the compositions of the two phases; (ii) Determine the weight fractions of the two phases Read from the tie line: 1455°C Liquid phase:Cu-30%Ni α-phase: Cu-55%Ni C0 Cs − Co 55 − 50 T1 CL WL = = = 0.2 = 20% Cs − CL 55 − 30 CS Co − CL 50 − 30 Wα = = = 0.8 = 80% 1085°C Cs − CL 55 − 30 or 30%Ni 55%Ni Wα = 1 − WL = 1 − 0.2 = 0.8 = 80% Cu 50%Ni Ni Cooling Curves determination of Phase diagrams II 1455°C 1085°C T Liquidus (thermal arrest) T1 Solidus T T2 I T1 1085°C T II I III T2 Cu % Ni t Eutectic Systems Pb-Sn phase diagram 350 The Pb-Sn system is characteristic of a valley in the Liquid 300 middle. Such system is known as Liquidus the Eutectic system. The 250 Temperature central point is the Eutectic Eutectic point and the transformation point α+L though this point is called 200 L+β Eutectic reaction: Lα+β 150 solidus β phase: solid Pb has a fcc structure and Sn has α phase: solid solution of Pb in a tetragonal structure. The 100 solution of Sn tetragonal Sn system has three phases: L, α and in fcc Pb β. solvus 50 α+β solvus 0 0 10 20 30 40 50 60 70 80 90 100 Pb Sn (Fcc) Wt% (Tetra) Solidification of Eutectic Systems Pb-Sn phase diagram Alloy I: 350 II I III At point 1: Liquid Solidiﬁcation starts at liquidus 1 Liquid At point 2: L+α 300 2 The amount α ↑ with ↓ T Solidiﬁcation ﬁnishes at solidus 250 Temperature At point 3: α 3 Precipitation starts at solvus α 200 At point 4: α+β β Further cooling leads to formation and growth of more β precipitates 150 whereas Sn% in α decreases following the solvus. 100 4 The cooling curve of this alloy is 50 similar to cooling curve I shown in slide 9. 0 0 10 20 30 40 50 60 70 80 90 100 Pb Sn (Fcc) Wt% (Tetra) (a) (1) L (2) L L α Precipitates in a Al-Si alloy; (a) optical microscopy, (b) scanning electron microscopy of fracture surface (3) (4) α β α (b) Solidification of Eutectic Systems Alloy II: Pb-Sn phase diagram At point 1: Liquid Solidiﬁcation starts at eutectic 350 point (where liquidus and solidus I III II Liquid join) 300 At point 2: L(α+β) (eutectic reaction) 250 1 Temperature The amounts of α and β increase in proportion with time. α Solidiﬁcation ﬁnishes at the same 200 β temperature. 2 At point 3: α+β 150 Further cooling leads to the depletion of Sn in α and the 100 depletion of Pb in β. 3 The cooling curve of this alloy is 50 similar to cooling curve II shown in slide 9. 0 0 10 20 30 40 50 60 70 80 90 100 Pb Sn (Fcc) Wt% (Tetra) (1) L (2) L L (3) Nucleation of colonies of α and β laminates Eutectic structure of intimate mix of α and β to Pb-Sn eutectic minimise diffusion path Solidification of Eutectic Systems Pb-Sn phase diagram Alloy III: At point 1: Liquid 350 Solidiﬁcation starts at liquidus I III II Liquid At point 2: LL+α (pre-eutectic α) 300 The amount α ↑ with ↓T 1 At point 3: L (α+β) (eutectic 250 Temperature reaction) Solidiﬁcation ﬁnishes at the eutectic α 2 temperature 200 β At point 4: α+β (pre-eutectic α + 3 (α+β) eutectic mixture) 150 Further cooling leads to the depletion of Sn in α and the depletion of Pb in 4 100 β. The cooling curve of this alloy is a 50 combination of the two cooling curves shown in slide 9. 0 0 10 20 30 40 50 60 70 80 90 100 Pb Sn (Fcc) Wt% (Tetra) (1) L (2) Cooling curve L L α (3) (3) Pr Cu-Ag alloy e- eu tec tic L Eut α α α Eutectic laminate of α and β Solidification of Eutectic Systems 350 I III II IV 300 Liquid Can you describe the 250 solidiﬁcation process of alloy IV, including microstructure evolution, morphology of phases 200 α β and cooling curve? 150 100 50 α+β 0 Pb Sn Hypoeutectic Hypereutectic Gibbs Phase Rule Gibbs phase rule F =C+N-P F: degree of freedom C: number of chemical variables N: number of non-chemical variables P: number of phases L one-phase region Application of Gibbs phase rule: For a binary system at ambient pressure: two-phase C=2 (2 elements) equilibrium (line) N=1 (temperature, no pressure) For single phase: F=2: % and T α (a region) β For a 2-phase equilibrium: F=1: % or T (a line) For a 3-phase equilibrium: F=0, (invariant three-phase point) equilibrium (point) May we have a 4-phase equilibrium, in a binary system, or in any system? α+β Pb Sn Non-Equilibrium Solidification Some transformations do not cause changes in composition, such as the solidiﬁcation of a pure metal, whereas some other do, such as the solidiﬁcation of an alloy into a solid solution. The former is known as congruent transformation and the latter incongruent transformations. Congruent transformations are cooling rate insensitive and incongruent transformations are cooling rate sensitive – they rely on interdiffusion to proceed. Solidiﬁcation under a fast cooling rate, where diffusion is insufﬁcient to homogenise the composition simultaneously during the process is known as the non-equilibrium solidiﬁcation. A common consequence of non-equilibrium solidiﬁcation is coring. Coring Alloy Co starts solidiﬁcation at T1. The ﬁrst Equilibrium solid formed has composition Cs1. On solidus Co further cooling to T2, an outer shell of composition Cs2 is formed surrounding T1 (start of solidification) Cs1 Cs1. Due to inadequate diffusion on fast Cs cooling, a composition difference is created. T2 The average composition of the solid 2 composite at T2 is, thus, somewhere Cs T3 (end of solidification under equilibrium) between Cs1 and Cs2: Cs2*. The same 2 * situation continues throughout the process. Cs Under equilibrium condition solidiﬁcation T4 (actual end of * solidification) completes at T3. However, under non- 3 equilibrium condition, the average Effective composition of solid at T3 is Cs3* <Co, solidus indicating that solidiﬁcation is not completed A %B yet. Solidiﬁcation actually ends when the average composition of solid equals Co, i.e., Non-equilibrium solidification lowers at T4. effective melting temperature. Coring T1 L T2 Equilibrium Cs1 Cs1 solidus Co T1 (start of solidification) Cs2 Cs1 Average solid composition: Cs2* Cs T2 T3 2 Cs T3 (end of solidification under equilibrium) * 2 Average solid Cs T4 (actual end of * solidification) composition: Cs3* 3 T4 Effective solidus A %B The cored structure: composition segregation, Average solid enrichment of high-Tm constituent in the core composition: Co Coring in Eutectic Systems According to the lever rule, the co L weight fraction of the eutectic products can be computed as: Under equilibrium condition: α β c−b a b c d Weut = d −b Under non-equilibrium condition: c−a α+β * W eut = d −a * A B Weut > Weut Coring leads to increase of weight fraction of eutectic products Constitutional Supercooling Co S L CS C CL CL Co CS x T Tm A %B T S L Supercooling window caused by x rising Tm, resulting in unstable interface Dendrite Structure of Metals A consequence of constitutional supercooling and destabilisation of solid-liquid interface is the formation of dendritic structure, as commonly found in alloy castings. In such structure, gaps between dendrites and between dentitic ﬁngers are regions rich of low-melting temperature phases and impurities. Dendritic branches themselves are often cored, too. This often require post-casting heat treatment to homogenise the structure.
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