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# Phase Diagrams

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### Phase Diagrams

1. 1. Phase diagrams
2. 2. PhaseA phase can be defined as a physically distinct and chemicallyhomogeneous portion of a system that has a particularchemical composition and structure.Water in liquid or vapor state is single phase. Ice floating onwater is an example two phase system.Gibbs Phase ruleThe number of degrees of freedom, F (no. of independentlyvariable factors), number of components, C, and number ofphases in equilibrium, P, are related by Gibbs phase rule asF = C – P + 2Number of external factors = 2 (pressure and temperature).For metallurgical system pressure has no appreciable effect onphase equilibrium and hence, F = C – P + 1
3. 3. Phase DiagramsOne component systemThe simplest phase diagram is the water which is a onecomponent system. It is also known as pressure-temperature orP-T diagram. Two phases exist along each of the three phaseboundaries. At low pressure (0.006 atm) and temperature (0.01C) all the three phases coexist at a point called triple point.Water phasediagram
4. 4. Binary Phase diagramsA binary phase is a two component system. Binary phasediagrams are most commonly used in alloy designing.The simplest binary system is the Cu-Ni which exhibitscomplete solubility in liquid and solid state.Cu-Ni equilibriumphase diagram
5. 5. Binary Phase diagramsThe line above which the alloy is liquid is called the liquidusline. At temperature just below this line crystals of  solidsolution start forming.The line below which solidification completes is calledsolidus line. Hence, only  solid solution exists at anytemperature below the solidus line.The intermediate region between liquidus and solidus linesis the two-phase region where liquid and solid coexist.It can be noted that the two metals are soluble in each otherin the entire range of compositions in both liquid and solidstate. This kind of system is known as ‘Isomorphous’ system.
6. 6. The Tie lineThe composition of phases in the two-phase region is notsame.To find the composition of the individual phases in the two-phase region, a horizontal line (XY), called tie line, is drawn andits intercepts on the liquidus and solidus lines, Cl and Cs, aretaken as the composition of the liquid and solid respectively.
7. 7. Lever ruleThe relative fractions of the phases at a given temperature foran alloy composition Co is obtained by the lever rule. This rulegives the fraction of a phase by the ratio of the lengths of the tieline between Co and composition of the other phase to the totallength of the tie line. For example, fraction solid, fs is given bylslosCCCCX YM XfSimilarly fraction liquid, fllsoslCCCCX YM Yf
8. 8. Cooling curvesUpon cooling from liquid state, the temperature of the puremetal (A or B) drops continuously till melting point at whichsolidification starts. Solidification happens at a constanttemperature (line PQ) as F =0 (F = 1 – 2 +1 = 0). Thetemperature drops again on completion of solidification.For any alloy (1, 2, 3 etc.) temp. drops till the liquidus (L1, L2,L3). However, in this case, solidification proceeds over a rangeof temperature as F = 1 (2 – 2 + 1 = 1). Once solidificationcompletes at the solidus (S1, S2, S3) the temp. drops again.
9. 9. Phase diagrams- Limited solubilityNot all metals are completely soluble in each other.Distinctions can be made between two types solid solutionswith limited solubility – (i) Eutectic and (ii) Peritectic.When the melting points of two metals are comparable, aeutectic system forms while a peritectic results when meltingpoints are significantly different.A eutectic reaction is defined as the one which generatestwo solids from the liquid at a given temperature andcomposition, L   + Peritectic is Liquid + Solid 1  Solid 2 (L +   )In both the cases three phases (two solids and a liquid)coexist and the degrees of freedom F = 2 – 3 + 1 = 0. This isknown as invariant (F = 0) reaction or transformation.
10. 10. Eutectic Phase diagramIn the eutectic system between two metals A and B, twosolid solutions, one rich in A () and another rich in B () form.In addition to liquidus and solidus lines there are two morelines on A and B rich ends which define the solubility limits B inA and A in B respectively. These are called solvus lines.
11. 11. Eutectic Phase diagramThree phases (L++) coexist at point E. This point is calledeutectic point or composition. Left of E is called hypoeutecticwhereas right of E is called hypereutectic.A eutectic composition solidifies as a eutectic mixture of and  phases. The microstructure at room temperature (RT)may consist of alternate layers or lamellae of  and .In hypoeutectic alloys the  phase solidifies first and themicrostructure at RT consists of this  phase (calledproeutectic ) and the eutectic (+) mixture. Similarlyhypereutectic alloys consist of proeutectic  and the eutecticmixture.The melting point at the eutectic point is minimum. That’swhy Pb-Sn eutectic alloys are used as solders. Other eutecticsystems are Ag-Cu, Al-Si, Al-Cu.
12. 12. Eutectic Cooling curvesWhile cooling a hypoeutectic alloy from the liquid state, thetemp. drops continuously till liquidus point, a, at which crystalsof proeutectic  begins to form.On further cooling the fraction of  increases. At any point, b,in the two-phase region the  fraction is given by the lever ruleas bn/mn.
13. 13. Solidification of proeutectic  continues till the eutectictemperature is reached. The inflection in the cooling curvebetween points a and e is due to evolution of the latent heat.At the eutectic point (e) the solidification of eutectic mixture(+) begins through the eutectic reaction and proceeds at aconstant temperature as F = 0 (2 – 3 + 1).The cooling behavior in hypereutectic alloy is similar exceptthat proeutectic  forms below the liquidus.For a eutectic composition, the proeutectic portion is absentand the cooling curve appears like that of a pure metal.Any composition left of point c or right of point d ( and single phase region respectively) will cool and solidify like anisomorphous system.Eutectic Cooling curves
14. 14. Peritectic Phase diagramL +   . An alloy cooling slowly through the peritecticpoint, P, the  phase will crystallize first just below the liquidusline. At the peritectic temperature, TP all of the liquid and  willconvert to .Any composition left of P will generate excess  and similarlycompositions right of P will give rise to an excess of liquid.Peritectic systems – Pt - Ag, Ni - Re, Fe - Ge, Sn-Sb (babbit).
15. 15. Monotectic Phase diagramAnother three phase invariant reaction that occurs in somebinary system is monotectic reaction in which a liquidtransforms to another liquid and a solid. L1  L2 + .Two liquids are immiscible like water and oil over certainrange of compositions. Cu-Pb system has a monotectic at 36%Pb and 955 C.Cu-Pd system –Monotectic portion
16. 16. Phase diagrams with intermediate phasesBinary system can have two types of solid solutions/phases– terminal phases and intermediate phases.Terminal phases occur near the pure metal ends, e.g.  and phases in the eutectic system.Intermediate phases occur inside the phase diagram and areseparated by two-phase regions.The Cu-Zn system contains both types of phases.  and are terminal phases and , ,  and  are intermediate phases.Intermediate phases form in ceramic phase diagrams also.For example, in the Al2O3 – SiO2 system an intermediatephase called mullite (3Al2O3.2SiO2) is formed.
17. 17. Intermediate phases - Cu-Zn Phase diagramCu-Zn phase diagram.  and  are terminal phases and, ,  and  are intermediate phases.
18. 18. Phase diagrams with compoundsSometimes a crystalline compound called intermetalliccompound may form between two metals.Such compounds generally have a distinct chemical formulaor stoichiometry.Example – Mg2Pb in the Mg-Pb system (appear as a verticalline at 81% Pb ), Mg2Ni, Mg2Si, Fe3C.Mg - Pb phasediagram
19. 19. Ternary Phase diagramA ternary or three component phase diagram has the form ofan triangular prism with an equilateral triangle as a base.Pure components are at each vertex, sides are binarycompositions and ternary compositions are within the triangle.The composition lines on the triangle is constructed fromprojections of surfaces.Wt.% Cp
20. 20. Ternary phase diagramThe temperature varies along the height of the prism. Thecomposition triangle is an isothermal section. Alternativelyprojections of different surfaces and lines can be shown astemperature contours.The composition of any point in the triangle is determined bydrawing perpendiculars from corners to the opposite sides andmeasuring the distance of the point along the perpendicular.Point p, for example, lies on the isocomoposition line 25% Aalong the perpendicular A-50. Hence, percentage of A in thealloy is 25%. Similarly B is 50% and C is 25%.
21. 21. ExamplesEx.1. A 53% Ni Cu-Ni alloy is cooled from liquid state to1300 C. Calculate the % of Liquid and solid at 1300 C.Solution: The tie line at 1300 C intersects solidus at 58% Niand liquidus at 45% Ni.Apply the lever rule to get the liquid fraction% Liquid = 100* (58 – 53)/(58 – 45) = 38%%Solid = 100* (53 – 45)/(58 – 45) = 62% (100 – %Liquid))Ex.2. A 34.6% Pb-Sn alloy is cooled just below the eutectictemperature (183 C). What is the fraction of proeutectic and eutectic mixture ( +)?Solution: The eutectic point is at 61.9% Sn and  boundaryis at 19.2% Sn. Apply the lever rule% proeutectic  = 100*(61.9 – 34.6)/(61.9 – 19.2) = 64%% ( +) = 100* (34.6 – 19.2)/(61.9 – 19.2) = 36%
22. 22. Referenceshttp://serc.carleton.edu/research_education/equilibria/phaserule.htmlhttp://www.sjsu.edu/faculty/selvaduray/page/phase/binary_p_d.pdfhttp://www.soton.ac.uk/~pasr1/eutectic.htmhttp://www.ce.berkeley.edu/~paulmont/CE60New/alloys_steel.pdfhttp://www.substech.com/dokuwiki/doku.php?id=phase_transformations_and_phase_diagramshttp://www.sjsu.edu/faculty/selvaduray/page/phase/ternary_p_d.pdf1. M. Hansen & K. Anderko, Constitution of Binary Alloys,McGraw-Hill, 19582. ASM International, ASM Handbook Volume 3: Alloy PhaseDiagrams, 1992Web References
23. 23. Key wordsKey Words: Phase; phase rule; phase diagrams; isomorphous;eutectic; peritectic; monotectic; intermetallic compound; ternaryphase diagram.
24. 24. Quiz1. Define a phase? What is Gibbs phase rule?2. What is isomorphous system? Give example of anispmorphous sytem.3. Why does a liquid metal solidify at constant temperature?4. What is a tie line. What is lever rule?5. How is the liquidus and solidus curves of a binaryisomorphous system determined experimentally? (Clue: Referto the cooling curves)6. What is an invariant reaction? Give some examples.7. What kind of system will result when melting points twometals having limited solubility in each other are (i) comparable(ii) significantly different?8. What is a solvus line?9. What is eutectic? Why there is infliction in the cooling curveof a hypoeutectic alloy in the two-phase region?
25. 25. Quiz10. Why does the eutectic reaction happen at a constanttemperature?11. Why Pb-Sn alloys are used as solders?12. What are terminal and intermediate phases?13. What is an intermetallic compound?14. What are the typical phases present in Brass (Cu-Zn)?15. How is the composition of an alloy determined in a ternarysystem?16. What is monotectic reaction?17. A Pb-Sn alloy contains 64 wt% proeutectic  and resteutectic (+) just below 183 C. Find out the averagecomposition. (Consult Example #2)18. A 35 wt% Ni Cu-Ni alloy is heated to the two-phase region.If the composition of the  phase is 70% Ni find out (i) thetemperature, (ii) the composition of the liquid phase and (iii) themass fraction of both phases. (Consult a Cu-Ni phase diagram)