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# Chap1,part2

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### Chap1,part2

1. 1. Second Chapter PHASE DIAGRAM
2. 2. Phase diagram• a phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically- distinct phases.• Phase Diagrams, which indicate the phases present at a given temperature and composition, have often proved a difficult concept to understand.• These are known as equilibrium diagrams. Temperature is plotted on or ordinate (y-axis) and composition (in binary phase diagram or pressure (unitary phase diagram) on abscissa (x-axis) in the phase diagram.• The compositions is expressed in % weight. Phase diagram are always drawn equilibrium state because the system always tries to be stable.
3. 3. Classification of phase diagrams• Unary phase diagram (single components system).• Binary phase diagram (two components system).• Tertiary phase diagram (three components System).• Quarter phase diagrams (four components systems).
4. 4. Unary phase diagram (single components system).The diagram indicateddifferent phases as afunction of temperature andpressures. Crystal form ofiron such as BCC(alpha,α), FCC (Gamma, γ)and HCC (Delta, δ) areobtain as increasing thetemperatures. The BCCform converted to HCPform near a pressure ofabout 125 atm. Above theeutectic point temperature,i.e., 9100C BCC convertedto FCC. at a peritectic pointtemperature, i.e., 14950Cliquid + HCP converted to Fig T-P phase diagram for iron. I am not sure that IFCP. believe that there is a critical point for liquid and γ-Temp range for Fe.BCC = upto 9100C.FCC = 920-14100C 0
5. 5. Binary phase diagram (two components system).Such diagram of results of two componentssystems. In addition pressure andtemperature, a third variable, composition isalso involved now. It therefore threedimensional diagram to depict phases.However for the simplicity of plotting phasediagrams on paper; the temperature isalways taken on ordinate and compositionon abscissa for a specified pressure.The binary diagram of two components areA and B. Percentage weight components.Percentage weight composions of A raiesfrom 0 to 100 from left to right while that of Bvaries from between 0 to 100 from right to A phase diagram for a binaryleft on horizental axis named as composition system displaying a eutecticor C axis. There are two phase regions, viz point. The eutectic point is thethe solid and liquid. The solid phase region point at which the liquid phaselies middle of the straight line called as tie- L borders directly on the solidline. The liquid phase region lies above the phase α + β.solid phase lines.
6. 6. Classification of binary phase diagram• Eutectic Phase diagram• Eutectoid phase diagram• Paritactic phase diagram• Peritectoid phase diagram
7. 7. Eutectic Phase diagram• An eutectic phase diagram is obtained when the melting point of the two components of the phase diagram are neither very close nor much different .• The eutectic system involves the transformation of a liquid phase into two other solid phases on cooling and vice versa, and expressed as• L (liquid phase) → α+β (solid Phase)
8. 8. Some uses of Eutectic phase diagram• Some uses include:• eutectic alloys for soldering, composed of tin (Sn), lead (Pb) and sometimes silver (Ag) or gold (Au).• casting alloys, such as aluminum-silicon and cast iron (at the composition for an austenite-cementite eutectic in the iron-carbon system).• brazing, where diffusion can remove alloying elements from the joint, so that eutectic melting is only possible early in the brazing process.• temperature response, i.e. Woods metal and Fields metal for fire sprinklers.• non-toxic mercury replacements, such as galinstan.• experimental metallic glasses, with extremely high strength and corrosion resistance.• eutectic alloys of sodium and potassium (NaK) that are liquid at room temperature and used as coolant in experimental fast neutron nuclear reactors.
9. 9. Eutectoid Phase diagram• In eutectoid system, a solid phase replaces the liquid phase of eutectic system.• The eutectoid system involves the transformation of a solid phase into two other solid phases on cooling and vice versa, and expressed as• γ (solid phase) → α+β (solid Phase).• In the Fe-C system, there is a eutectoid point at approximately 0.8wt% C, 723°C.
10. 10. The compositions of thetwo new phases are given by the ends of the tie-line through the eutectoid point. The general eutectoid reaction is therefore:Solid γ –> solid α + solid β or using the names given to these phases: Austenite –> ferrite + cementite (Fe3C)
11. 11. EutectoidWhen the solution above thetransformation point is solid, rather thanliquid, an analogous eutectoidtransformation can occur.For instance, in the iron-carbon system,the austenite phase can undergo aeutectoid transformation to produceferrite and cementite (iron carbide),often in lamellar structures such aspearlite and bainite.This eutectoid point occurs at 727°C(1340.6 ºF) and about 0.83% carbon[5];alloys of nearly this composition arecalled high-carbon steel, while those Iron-carbon phase diagram, showingwhich have less carbon are termed the euctectoid transformationmild steel. The process analogous to between austenite (γ) and pearlite.glass formation in this system is themartensitic transformation.
12. 12. Paritactic phase diagram• Peritectic transformations are also similar to eutectic reactions. Here, a liquid and solid phase of fixed proportions react at a fixed temperature to yield a single solid phase.• L + β phase → α Phase• Since the solid product forms at the interface between the two reactants, it can form a diffusion barrier and generally causes such reactions to proceed much more slowly than eutectic or eutectoid transformations. Because of this, when a peritectic composition solidifies it does not show the lamellar structure that you find with eutectic freezing.• Such a transformation exists in the iron -carbon system, as seen near the upper-left corner of the figure. It resembles an inverted eutectic, with the δ phase combining with the liquid to produce pure austenite at 1495 °C and 0.17 mass percent carbon
13. 13. • Peritectic• Peritectic transformations are also similar to eutectic reactions.• Here, a liquid and solid phase of fixed proportions react at a fixed temperature to yield a single solid phase. Since the solid product forms at the interface between the two reactants, it can form a diffusion barrier and generally causes such reactions to proceed much more slowly than eutectic or eutectoid transformations. Because of this, when a peritectic composition solidifies it does not show the lamellar structure that you find with eutectic freezing.• Such a transformation exists in the iron-carbon system, as seen near the upper-left corner of the figure. It resembles an inverted eutectic, with the δ phase combining with the liquid to produce pure austenite at 1495 °C and 0.17 mass percent carbon.
14. 14. Peritectoid phase diagram• Peritectoid phase diagrams involve transformation of two solid phases into a different solid phase on cooling and vise versa. Contrary peritectic reaction where sodid liquid phase L + β changed to another solid phase α; here solid phase changed to another solid phase. It is given by• γ + β phase → α solid Phase
15. 15. Gibbs phase rule• Gibbs phase rule, stated by Josiah Willard Gibbs in the 1870s, is the fundamental rule on which phase diagrams are based. F=2−π+C• where π is the number of phases present in equilibrium (Types of solid, liquid, gas phases etc). F is the number of degrees of freedom or independent variables taken from temperature, pressure and composition of the phases present. C is the number of chemical components required to describe the system
16. 16. • Condensed phase rule• In many solids with high melting temperature; the vapour pressure of the solids and even that of the liquid is negligible in comparison with atmospheric pressure. F=1−π+N
17. 17. Figure 1 shows theequilibrium diagram forcombinations of carbon in asolid solution of iron. Thediagram shows iron andcarbons combined to formFe-Fe3C at the 6.67%C endof the diagram. The left sideof the diagram is pure ironcombined with carbon,resulting in steel alloys.Three significant regions canbe made relative to the steelportion of the diagram. Theyare the eutectoid E, thehypoeutectoid A, and thehypereutectoid B. The rightside of the pure iron line iscarbon in combination withvarious forms of ironcalled alpha iron (ferrite),gamma iron (austenite),and delta iron. The blackdots mark clickablesections of the diagram. Fig 1: Fe-Fe3C Phase Diagram Iron-Iron Carbide Phase Diagram
18. 18. Continue...• Allotropic changes take place when there is a change in crystal lattice structure. From 2802º-2552ºF the delta iron has a body-centered cubic lattice structure.• At 2552ºF, the lattice changes from a body-centered cubic to a face-centered cubic lattice type.• At 1400ºF, the curve shows a plateau but this does not signify an allotropic change. It is called the Curie temperature, where the metal changes its magnetic properties.• Two very important phase changes take place at 0.83%C and at 4.3% C. At 0.83%C, the transformation is eutectoid, called pearlite.• gamma (austenite) --> alpha + Fe3C (cementite)• At 4.3% C and 2066ºF, the transformation is eutectic, called ledeburite.• L(liquid) --> gamma (austenite) + Fe3C (cementite)
19. 19. Home assignments• Equilibrium Calculations 1. Given the Fe-Fe3C phase diagram, Fig. 1, calculate the phases present at the eutectoid composition line at: a. T = 3000ºF b. T = 2200ºF c. T = 1333ºF d. T = 410ºF 2. Calculate the phases in the cast-iron portion of the diagram at the eutectic composition of 4.3% C in combination with 95.7% ferrite at: a. T = 3000ºF b. T = 1670ºF c. T = 1333ºF 3. A eutectoid steel (about 0.8%C) is heated to 800ºC (1472ºF) and cooled slowly through the eutectoid temperature. Calculate the number of grams of carbide that form per 100g of steel. 4. Determine the amount of pearlite in a 99.5% Fe-0.5%C alloy that is cooled slowly from 870ºC given a basis of 100g of alloy.
20. 20. Lever Rule• To determine compositions of phases and the relative proportions of phases to each other in Binary diagrams the LEVER RULE is used.• Using the lever rule one can determine quantitatively the relative composition of a mixture in a two-phase region in a phase diagram. The distances l from the mixture point along a horizontal tie line to both phase boundaries give the composition:• Nα lα = nβ lβ• nα represents the amount of phase α and nβ represents the amount of phase β.
21. 21. 1. Point "I" lies above the liquidus within theliquid field.What is the composition, in terms of the two endmember components, A and B, of the liquidrepresented by this point?To determine the composition of "I" you mustcomplete the following steps:1. Draw a line through "I" perpendicular to theAB join, i.e., the base of the diagram. This linerepresents a line of constant composition and isreferred to as an isopleths.2. The liquid at "I" consists of a mixture of A andB, the proportions of which can be determinedsimply by measuring the length of three lines,AI, BI and AB and then ratio these lengths.%A = IB/AB *100%B = IA/AB *100This gives us the bulk composition of the liquidat this point. If the composition point for themoves then we get a new bulk composition forthat point represented by the new liquid
22. 22. Home Assignment